Which structure of a paramecium plays a major role in sexual reproduction?

Paramecia are ciliated protists.  Paramecium reproduce basically asexually by bipartition (binary fission). In this process a cell duplicates its genetic material and divides into two, each with half the cellular organelles that the progenitor cell.

Paramecium can also, occasionally, exchange genetic material with another paramecium by conjugation, a primitive form of sexual reproduction. Two parameciums found can combine their membranes to form a large paramecium with two nuclei that contain all the genetic material. This large paramecium will be divided into four new cells each with a new combination of DNA from the DNA combination of the progenitor cells.