CATANIA, Italy — The mother had prepared everything for the baptism. She dressed her infant son Antonio in a handmade satin suit with tails and a matching cream-colored top hat glittering with rhinestones. She hired the photographers and bought the baby a gold cross. She booked a big buffet lunch for the whole clan at the Copacabana.

But as the parish priest in the Sicilian city of Catania went through the usual liturgy, calling on the family to renounce Satan and ladling holy water on the squirming baby’s head, one major part of the ritual went missing.

There was no godfather.

“It’s not right,” said Agata Peri, 68, little Antonio’s great-grandmother. “I definitely didn’t make this decision.”

The church did. That weekend in October, the Roman Catholic diocese of Catania enacted a three-year ban on the ancient tradition of naming godparents at baptisms and christenings. Church officials argue that the once-essential figure in a child’s Catholic education has lost all spiritual significance. Instead, they say, it has become a networking opportunity for families looking to improve their fortunes, secure endowments of gold necklaces and make advantageous connections, sometimes with local power brokers who have dozens of godchildren.

God parenting, church officials said, had fallen to earth as a secular custom between relatives or neighbors — many deficient in faith or living in sin, and was now a mere method of strengthening family ties.

And sometimes mob ties, too.

Italian prosecutors have tracked baptisms to map out how underworld bosses spread influence, and mob widows in court have saved their most poisonous spite for “the real Judases” who betray the baptismal bond. It is a transgression most associated with, well, “The Godfather,” especially the baptism scene when Michael Corleone renounces Satan in church as his henchmen whack all of his enemies.

But church officials warn that secularization more than anything led them to rub out the godparents, a Sicilian thing that’s been going on for 2,000 years, or at least since the church’s dicey first days, when sponsors known to bishops vouched for converts to prevent pagan infiltration.

“It’s an experiment,” said Msgr. Salvatore Genchi, the vicar general of Catania, as he held a copy of the ban in his office behind the city’s basilica. A godfather to at least 15 godchildren, the monsignor said he was well qualified for the role, but he estimated that 99 percent of the diocese’s godparents were not.

The break would allow the church some time to send Catania back to Catholic school, but Monsignor Genchi was not optimistic that it would stick. “It seems very difficult to me,” he said, “that one can turn back.”

In 2014, Archbishop Giuseppe Fiorini Morosini of Reggio Calabria, where the ’Ndrangheta mob is rooted, proposed a 10-year stop on godfathers, arguing in a letter to Pope Francis that a secular society had spiritually gutted the figure. That, he said, also made it ripe for exploitation by mobsters.

Archbishop Morosini said that a top Vatican official, Cardinal Giovanni Angelo Becciu, who is now on trial in the Vatican on money laundering charges, responded that all of Calabria’s bishops needed to agree before moving ahead. They did not.

But Archbishop Morosini said he kept bringing the issue up with Francis, who “showed himself very attentive” to it, and, in a meeting in May, told him, “‘Every time I see you, I remember the godfather problem.’”

The Rev. Angelo Alfio Mangano, of the Saint Maria in Ognina church in Catania, welcomed the ban, especially because it gave him a rest from spiritually questionable characters using “threats against the parish priest” to pressure him and others into naming them godfather.

Sometimes, he said, the position was used for social blackmail and usury, but mostly it became a method to enforce Sicily’s entrenched culture of ritual kinship.

“It creates a stronger tie between the families,” said Nino Sicali, 68, as he sliced a swordfish with a machete at the Catania fish market. When he was made a godfather, he said, he reciprocated by making his godson’s father a “compare” — or co-father — to his own children. Over the years, Mr. Sicali said he was obligated to help his struggling compare out financially. “He died owing me 12,000 euros,” he said.

Some families sought out godfathers who opened doors.

Salvatore Cuffaro, a former president of Sicily, said that he did not have many baptismal godchildren, “just about 20,” agreeing to only about 5 percent of requests. He was sought after, he said, for his “Christian principles,” demonstrated over decades of political life.

“Despite what some priests think, I paid attention to all of my baptismal godchildren” and instructed them to go to Catholic school, he said.

Mr. Cuffaro, nicknamed “Kiss Kiss” for his tendency to kiss everyone, served nearly five years in prison for helping alert a mafia boss that he was being wiretapped. He denied those charges and that a Mafioso had ever served as godfather to anyone on the island.

“At least in Sicily, where I have lived, this doesn’t exist,” he said. “It’s only a religious bond; there are no bonds of illegality.”

He worried that by getting rid of the tradition, the church was “throwing the baby out with the bathwater.”

Parents baptizing their children in churches across Catania on the first Sunday of the ban were likewise appalled at the loss of a beloved tradition.

“It’s shocking,” said Jalissa Testa, 21, who celebrated her son’s baptism at the Catania basilica by dancing as her husband serenaded a crowd of women waving white napkins. “In our hearts we know, and they will know, that he has a godfather.”

Marco Calderone carried his 6-month-old son, Giuseppe, past a newspaper clipping on the wall of the Saint Maria in Ognina church reading, “Baptisms and Christenings: Stop to Godfathers and Godmothers.”

“For them it might be abolished,” Mr. Calderone said. “Not for us.”

Afterward, the family posed on the church steps, and the family photographer (“You see the necklace on that baby?” the photographer said) called for the godfather to join.

“Salvo,” Mr. Calderone shouted, beckoning the unofficial godfather to join them.

Even the family that received special dispensation to have a godfather because a death in the family had delayed their previously scheduled baptism was vexed by the rule.

“I don’t understand why the church is doing this,” Ivan Arena, 29, who may be the last godfather of Catania, said after the baptism of his nephew, who was dressed in a three-piece powder blue suit and white coppola cap. “I’m for the old traditions.”

After that ceremony, the priest turned to the family across the central nave. The women shimmered in sequins and the men wore monkish mullets — short in the front, long in the back, shaved around the ears. They received no such allowance.

“What difference does it make,” said the proud father, Nicola Sparti, 24, who described his occupation as “a little bit of this, a little bit of that.” (“Flees from Carabinieri on a motorbike,” read a recent newspaper article about him.) “One day the godfather’s there and the next he’s gone. But a father is forever.”

Mr. Sparti and his wife then drove to the nearby city Aci Trezza for a photo shoot in front of the three majestic sea rocks that, legend has it, the Cyclops heaved at the fleeing Odysseus. They put Antonio in a miniature, remote-controlled white Mercedes and cheered as he cruised the port.

Above them, the Rev. Giovanni Mammino, the city’s vicar general, came out of the St. John the Baptist church after celebrating a christening. His diocese required forms from godfathers swearing that they were believers and not Mafia members. Unlike Catania, he said, his diocese had taken a middle road, allowing godparents, but not requiring them.

Now, people are slipping over the Catania border for baptisms.

“They keep coming here so that they can have the godfathers,” he said.

The Sparti family, though, had played by the rules and came only for lunch. They drove to the nearby Copacabana, where they celebrated with heaping plates of pistachio pasta, cake, gifts and generations of parents and godparents.

Alfio Motta, 22, Antonio’s uncle, watched it all from the D.J. console, thinking of what could have been.

“I feel like the godfather,” he said. “Even if I don’t have the title.”