CLEVELAND (AP) _ Police, ordered by the mayor to find four people who donned sheets and burned a cross on a black family's yard, arrested three white teen-agers Thursday in the incident.

Two of the three youths were held in detention and the other was released to his parents, police spokesman Robert Bolton said. Two of the boys are 13 years old, and the other 15.

The incident in a white enclave of the predominantly black Collinwood neighborhood ''left a feeling of anger and disgust'' among blacks there, said Councilman Larry A. Jones.

Earlier, Mayor George Voinovich ordered police to find the culprits.

''All you can do is put your people on it, and that's what he has done,'' said Claire Rosacco, the mayor's press secretary. ''I'd say he was absolutely visibly upset and just couldn't believe people would do that.

''He was outraged.''

Frances Lampley told police she looked outside Tuesday night and saw the burning cross and four people wearing sheets. Three of them ran. The fourth, a man, shielded his face, took off the sheet and tossed it at the burning cross.

Mrs. Lampley said the man yelled, ''This will be your last warning.''

On Wednesday, Voinovich ordered police Chief William T. Hanton to find those responsible.

''This cruel and unthinking act is an embarrassment to, and bad reflection on, the entire Cleveland community, particularly the Collinwood area, and it will not be tolerated,'' the mayor said.

Police and FBI agents interviewed neighbors Wednesday and looked for clues.

Since buying their home in the neighborhood two years ago, the Lampleys have been victimized by countless other incidents, including from racial taunts and threats, said Mrs. Lampley's husband, James. He and his wife have their 4-year-old daughter.

The cross burning was one of many racial incidents reported this year against blacks in the city. In 1984, 24 incidents of racial harassment were reported. There have been 46 this year, said Earl Williams, the city's director of community relations.

Williams said most of the incidents have been reported in areas where blacks have moved into white enclaves.

''We have not had these kinds of acts, like people appearing in sheets. We are very, very concerned about it,'' Williams said.

In the past, Voinovich has been criticized by members of City Council, who alleged he was not outspoken enough against racially motivated crimes. The criticism stemmed largely from the city's inability to find the murderer of Mabel Gant, an elderly black woman slain last summer in the city's mostly white Slavic Village neighborhood.