The translation of the phrase is "There's something of Piron inside of him," and as near as I can figure out Piron is "Alexis Piron," who is known as an "epigrammatist and dramatist." Piron rose to fame when me made an acclaimed one man show about Deucalion after the Deluge. He was "intimate" with two women, one of whom he married 20 years into their relationship.
The person who Dostoevsky says has a bit of Piron inside of him is Alexey's monk boss (?) who Alexey's dad is making fun of at the dinner when he (the dad) is drunk on brandy. So now you know.