The Belfast Telegraph and News Letter both lead with a report on Jim Allister's accusation, made under parliamentary privilege, that a former special adviser to Arlene Foster, Stephen Brimstone, used an RHI-funded boiler to heat his home.
Mr Allister said that Mr Brimstone's RHI claim was "the sort of rip-off that brings disrepute to all of the scheme". The DUP has said that Mr Brimstone is not intending to make a statement about the allegations.
Elsewhere on the News Letter's front page, the paper says that three men accused of terrorism offences in the last few months have received "paltry sentences".
The story is continued across the first five pages of the paper - inside, DUP MLA Nelson McCausland says that the sentencing is "not severe enough".
In the Daily Mirror, the investigation into the shooting of a PSNI officer on Sunday continues to dominate.
The paper leads with an appeal from the PSNI to trace the "ambush car" believed to have been used in the attack.
In the Irish News, Allison Morris writes that the attack showed that people could "exploit gaps in security".
She added that the shooting "appeared to take advantage of officers frequently using the shop" and that it shows it is "almost impossible to thwart every attack".
The papers also devote plenty of coverage to the appointment of Michelle O'Neill as Sinn Féin's northern leader.
The Daily Mirror reflects on a day described by Mrs O'Neill as "the biggest honour of my life".
It's a theme also picked up by the Irish News. The newspaper's political correspondent, John Manley, writes that Mrs O'Neill has "the potential to grow into her challenging role".
"In the coming months, it's doubly important that she lives up to the party leadership's high expectations," he writes.
And finally, boxing fans, could Windsor Park host a blockbuster bout in the future?
That's the speculation on the back page of the Belfast Telegraph, which claims Carl Frampton could face a unification fight with Lee Selby if they both can overcome their opponents this weekend.
"I want to have three fights this year and a fight with Selby at Windsor would be perfect," says Frampton.
He'll have to be beat Leo Santa Cruz on Sunday morning first, but if he does then Windsor could be a winner.
The investigation into the shooting of a police officer on a Sunday and the latest twist in the RHI scandal are taking up plenty of space on Tuesday's front pages.