AUSTIN (AP) _ The bribery trial of Attorney General Jim Mattox enters its third week Monday, with the prosecution continuing to present evidence alleging that the state official threatened lawyers who questioned his sister on a case.

Mattox, 41, was charged with commercial bribery in a Travis County District Court trial that is expected to last two more weeks. If convicted, he could be sentenced to 10 years in prison and a $5,000 fine.

He is accused of threatening to destroy the lucrative bond business of Fulbright & Jaworski, a Houston law firm, unless one of its lawyers stopped trying to question his sister, Janice Mattox, in an unrelated case.

Mattox has said the disagreement was only ''a spittin' contest between lawyers,'' and steadfastly maintains his innocence.

But two Fulbright & Jaworski lawyers, Wiley Caldwell and Thomas McDade, testified Mattox meant to ruin their bond business.

Caldwell, the firm's top bond lawyer, testified that Mattox called him several times in 1983 and threatened to ''go to war'' with the Houston firm.

Caldwell said Mattox asked him to ''muzzle McDade,'' and threatened to withhold approval of more than $300 million in public bonds the firm had pending in the attorney general's office. Under state law, the attorney general must approve such bonds before sale.

The questioning of Mattox's sister, Dallas lawyer Janice Mattox, came in connection with a suit filed by Texas oilman Clinton Manges against Mobil Oil Corp., according to Travis County District Attorney Ronnie Earle.

McDade, representing Mobil, sought to have state District Judge Ruben Garcia of Laredo disqualified because the judge had gotten a campaign contribution from a Manges-financed political action committee.

Mattox also got campaign money from Manges, prosecutors said. In addition, the state, which shares in oil revenue and is represented by the attorney general, joined the suit on Manges's side.

In the attempt to disqualify Garcia, McDade tried to question Miss Mattox about a $125,000 loan she and another brother, Jerry Mattox, received from a Seattle bank with which Manges was doing business.

Caldwell testified that on June 17, 1983, Mattox threatened to withhold approval of the firm's bonds.

Mattox, Caldwell testified, ''said until we got that matter straightened out, there would be no bond approvals from his office.''