It was a day for heroes at the White House yesterday as President Reagan awarded the Young American Medal for Bravery to three men and the parents of a fourth who died while rescuing a child.

The awards ceremony came 24 hours after the president's call to Reginald Andrews, an unemployed New York City man who rescued a blind passenger who had fallen between the cars of a subway train Monday. Reagan called Andrews after reading about how the father of eight, on his way home from a job interview, had saved the victim from serious injury.

Reagan thanked Andrews, 29, for his bravery, and called the meat-packing company where Andrews had applied for work to urge that he be hired. Reagan was told that the company planned to hire Andrews, and a company official quoted Reagan as saying, "Bless you."

A White House aide said he is pleased with widespread media interest in the president's effort on behalf of an unemployed, black father of eight. The aide said this Christmas story is much better than the Thanksgiving news from the White House that Reagan was considering a plan to tax unemployment benefits.

Yesterday, Reagan appeared on the verge of tears as he presented the awards for bravery. When he described how Jeffrey M. Jones, then 18 and a volunteer fireman from Lancaster, Pa., had died last year in the rescue of an 8-year-old boy who fell into an underground gas tank, the president's voice became heavy with emotion.

Jones' mother, Roseann, said that she started to cry because she saw the president's eyes fill with tears as he presented the citation.

"I guess I got worked up to see that the president felt . . . the president of the United States understood the pain," she said after the ceremony. "It doesn't stop the hurting. It's hard around the holidays and his birthday. He was our only child . . . , but it helps to know that other people care."

Another person honored for 1981 was Mark Rhinier, 19, who helped Jones rescue the child.

One winner of a medal for 1980 was Michael Browne of Dixon, N.M., who was 13 when he climbed a slippery mountain ledge in darkness to help rescue a climber with broken ankles.

Reagan praised Browne, saying he lives in an adobe house with no electricity and "very little of what we think young people need to grow up right. Well, I guess we're wrong. The grown men and women who know this young man. . . will tell you they don't come any better."

The other 1980 winner was Robert Noble of Fredonia, N.Y., 18 when he entered a burning car several times and rescued three passsengers, one of whom survived. Noble did so, Reagan said, even though his friends told him not to get involved because he could be sued by someone in the car.

"Heroes may not be braver than anyone else," the president told Noble. "They're just braver five minutes longer. You were brave five minutes before, too."

The president awarded Young American Medals for Service to Jeffrey Blake, 20, of Altoona, Pa., for designing a disaster response system for the American Red Cross, and to John Terry, 18, of Philadelphia, for spearheading work to keep neigborhood streets clean.