Could non wearing of supporter (under wear for men ) affect my fertility?

There is evidence that there is NO significant effect either way. You may be interested in reading the abstract of a study cited below. From it: "The hyperthermic effect of brief style underwear has been exaggerated. In our study there was no difference in scrotal temperature depending on underwear type. It is unlikely that underwear type has a significant effect on male fertility. Routinely advising infertility patients to wear boxer shorts cannot be supported by available scientific evidence." That is, underwear did not have a significant effect on temperature of the scrotum... and therefore should not effect the fertility of the wearer.

False. The evidence is, rather, that raising the temperature of the testes decreases sperm production, and wearing close fitting shorts tends to increase the temperature of the area.