Melléthei-Barna is a founding member of the Tisza Party.
He served as the party's legal director since its formation in 2020.
His withdrawal raises questions about political nepotism.
Family affair: Péter Magyar's brother-in-law withdraws name as Hungary's justice minister
Melléthei-Barna, a lawyer and university peer of Hungary's next prime minister, steps back from the nomination amidst political ties.