BRAXTON OUTPOINTS SCOTT IN PRISON BOUT

Dwight Braxton, who lived in the Rahway State Prison here nine years ago, returned today and, before suffering an attack of claustrophobia, scored a clear and unanimous decision over James Scott in a nationally televised light-heavyweight fight.

Braxton, who cut his right hand peeling potatoes in training camp two weeks ago, relied mainly on his left jab to outpoint a surprisingly retreating Scott.

''It's a good feeling coming back a success,'' said Braxton, who served two and a half years of a five-and-a-half-year sentence for armed robbery at this maximum-security prison where Scott, who is serving a life sentence for murder, had scored many impressive victories over leading contenders who later said they were ''intimidated'' by the atmosphere.

Braxton was not intimidated, but he did leave without taking a shower, and as he waited for guards to open another in a series of barred gates, he told reporters:

''You're in my way. I'm getting claustrophobia. I want out of here.'' Braxton Now 15-1-1

Referee Larry Hazzard gave the decision to Braxton, 175 pounds, by five rounds to four with one even. Both judges, Charles Spina and Frank Brunnett, had it 6-3-1 as 28-year-old Braxton raised his record to 15-1-1. Scott, 176, the most famous product of the prison's boxing program, lost only his second decision against 19 victories and a draw.

Braxton's victory, following a seventh-round knockout of Mike Rossman, the former champion, assured him of an eventual chance at the World Boxing Council light-heavyweight title, said Murad Muhammad, who promoted today's bout and will also stage Matthew Saad Muhammad's defense Oct. 3 against Jerry Martin.

Murad Muhammad said he thought Scott boxed cleverly. Scott, who says he is 33, had enough stamina to fight mostly on the run instead of with his customary forward march. ''Otherwise, I think Braxton would have knocked him out,'' Murad Muhammad said.

''He surprised me with the leg movement, in and out,'' said Braxton, ''but I quickly adjusted. It was obvious he was trying to survive. He knew if he had stayed inside, I would've knocked him out. He could've won a track meet today.

''He's nothing. He's just another fighter. He's slow as mollasses, has no good skills. He's just tough and in shape.'' Scott Circles on Outside

Braxton, who at 5 feet 8 inches is three inches shorter than Scott, beat Scott to the jab consistently. Scott circled on the outside, only occasionally planting himself suddenly to throw a jab, followed by a straight right. Most of these combinations were picked off by Braxton, who meanwhile continued to build up points, pressing to get inside where he would land a few body punches before being tied up.

It was not until the seventh round that Scott tried backing up Braxton, and as soon as he did, Braxton landed a solid right hand to the visitor's ear.

Scott fought well in the later rounds as Braxton tired, and Scott thought he had won. He polled a group of reporters in an office set up as an interview room, and only one had scored the fight in his favor. ''Well, there's one smart guy at least,'' said Scott.

Michael Katz