A 41-year-old ex-con was busted for the execution-style slaying of a Staten Island livery cab driver - who was killed while working a rare night shift so he could spend time with his daughters, police said yesterday.

Eldred Leitzsey's arrest for the seemingly random murder brought great relief to the cabbie's family, who heaped praise on cops yesterday.

"Two police officers came to me and they promised they would work so hard to get my husband's killer," Kwame Appeigyei's widow, Betty, told the Daily News. "They kept their promise. God bless them."

Appeigyei, 55, was shot in the back of the head early Wednesday after picking up two separate fares at the Staten Island ferry terminal.

Along with being charged with murder, Leitzsey of Staten Island is suspected of recently stabbing two other people in separate attacks near Park Hill Ave., where Appeigyei lived, police said.

On Wednesday, Leitzsey allegedly robbed a fellow passenger in the back of Appeigyei's taxi at 3 a.m. and then shot the cabbie while trying to get him to hand over his wallet. "The cabbie either refused to give it up or moved too slowly," a law enforcement source said yesterday.

Appeigyei's taxi veered out of control after the shooting, breaking through a fence before roaring up a staircase outside a building at Vanderbilt and Tompkins Aves. He died inside the car.

The other unidentified passenger wasn't hurt, but was covered in the cabbie's blood. Cops have cleared the second passenger of any wrongdoing.

His account of the killing and surveillance footage from a camera at the Staten Island ferry terminal helped cops identify Leitzsey as a suspect.

NYPD narcotics, housing and precinct cops - who knew Leitzsey from prior run-ins - passed his name along to homicide detectives, who, acting on a hunch, arrested him "at one of his Times Square hangouts" about 11:30 p.m. Friday, a police source said.

"It is wonderful," the cabbie's widow told The News. "This is very great news for the whole America because when people like this kill someone, they may kill someone else."

Appeigyei, a native of Ghana, usually drove his taxi during the day, but altered his routine to spend time with his two daughters - Angela, 18, and Alexandra, 12 - who were home on Easter break. The cabbie and his wife have three children, and he has four kids from a previous relationship.

Leitzsey, who was waiting to be arraigned yesterday, claimed after his arrest that he lives with his niece in Tribeca. But cops said he is estranged from his family and lives on Staten Island. His criminal history dates to 1982 and includes arrests for robbery, burglary and assault.

His niece, Tami Leitzsey,27, who had allowed him to stay temporarily at her N.Moore St. home, said she hadn't seen him in almost two years. "He told us he was living in Connecticut, but we never really believed him," she said. "He's always had a rough time."