Teen-age fathers are more likely to have experienced trouble with the law and in school than counterparts without children, according to a study of more than 1,300 young men.

The findings suggest that "there are various problem behaviors that seem to cluster together," including teen fatherhood, school problems, drugs and delinquency, said study director Arthur Elster, a pediatrician and visiting researcher at the National Institute of Child Health and Human Development. The study was funded by the federal Office of Population Affairs and the William T. Grant Foundation.

It was based on the National Longitudinal Survey of Work Experience, started by the Labor Department in 1979, in which a nationally representative sample of people age 14-21 in 1979 was surveyed annually to see what had happened in their lives, Elster said.

Of about 6,400 young males in the sample, 367 reported in 1980 that they had fathered a child before age 19. Thirty-two percent of the 367 were married.

The characteristics of the 367 teen-age fathers were compared with those of 1,000 nonfathers selected at random from the same sample of 6,400, Elster said. Results showed the following differences:

About 60 percent of white teen-age fathers and half of black and Hispanic teen-age fathers reported brushes with the law other than for traffic violations, from apprehensions to formal charges or convictions. Among nonfathers, about one-third had such legal troubles.

67 percent of white teen-age fathers and about 57 percent of black and Hispanic fathers had used marijuana at least moderately. Usage among nonfathers was 52 percent for whites and about 42 percent for blacks and Hispanics.

55 percent of white teen-age fathers, 65 percent of the blacks and 42 percent of the Hispanics had been expelled from school at least once, far more than the nonfathers.

Average income of the teen-age fathers' parents was $10,800 a year, compared with $15,600 for that of nonfathers.

Elster said the study seems to indicate clearly that "fatherhood status among adolescents appears to be a marker of problem behavior which is associated with other dysfunctional behaviors."

Elster noted that the study results are not all pessimistic. "This says 50 percent of these fathers are adjusting very well, and we should be optimistic about their ability to adjust to parenthood and support their families," Elster said.