He made the demand in a petition addressed to the Chairman, Board of Trustees of the Association on Monday.
Olumide Akpata had defeated Adesina and Babatunde Ajibade (SAN), to emerge the 30th NBA President.
However, in the petition, Adesina alleged that the election was tainted by over-voting, disenfranchisement of some eligible voters.
He also alleged that there was non-compliance with the provisions of the NBA constitution.
“It is needless to say, Mr Chairman and other members of the Board of Trustees of the NBA, that if the process is wrong, the product cannot be right. If the election process is wrongful and unconstitutional, the outcome must suffer the same fate and be cancelled.
“Since 2016 when this electronic voting system started, there have been consistent allegations of system manipulation and rigging which has resulted in litigation over NBA elections,” the petition read in part.
Adesina added that, “The time has come to regain the integrity of the Nigerian Bar Association by putting an end to unconstitutional and fraudulent elections in our association.”