The Princeton grad who allegedly killed his hedge-fund-founder dad who cut his allowance by $200 will undergo another psychiatric exam — as prosecutors revealed Tuesday that he swallowed a battery while locked up at Rikers Island.

An attorney for Thomas Gilbert Jr. told Manhattan Supreme Court Judge Melissa Jackson that his client is mentally ill and has even bizarrely requested the Iraqi consulate be subpoenaed as a witness in his case.

“It suggests acute psychosis. He can’t communicate with me. He’s completely unfit” to stand trial, said attorney Alex Spiro.

Prosecutor Craig Ortner admitted that Gilbert — who previously complained he was being “poisoned” by radioactive fallout at Rikers — ingested the battery last spring.

But Ortner fought against ordering yet another psych test, saying the court has been misled by Gilbert’s strange behavior.

“I don’t think there’s any basis . . . to order another 730 [psych] exam,” the prosecutor said. Ortner also disputed the notion that Gilbert has repeatedly called the president of Cablevision because he’s disturbed — saying Gilbert has been trying to obtain phone records as part of his case. “Phone records — not TV records,” Ortner said.

Gilbert was found mentally fit in December. He allegedly murdered Thomas Gilbert Sr. after the dad slashed his $2,400 monthly allowance in January 2015. Gilbert Sr., 70, founded the hedge fund Wainscott Capital.