Fish oil supplements improve testicular health
Young men who take a fish oil supplement have larger testes and produce more semen than men who don't take fish oil supplements. Researchers from the University of Southern Denmark report this in JAMA Network Open.
Nutrition & fertility
Multiple studies have shown an association between nutrition and fertility. These studies suggest that a diet with many whole grain products, vegetables, fruit, low-fat dairy, chicken, turkey, fish and shellfish has a positive effect on fertility. [Am J Obstet Gynecol. 2018;218(4):379-389.]

On the other hand, a diet with lot of processed meat products, soy, potato products, foods with a lot of sugar, alcohol and of course trans fatty acids may have a negative effect on fertility.
Food components that stimulate sperm quality in animal studies are vitamins C, D and E, folic acid, beta-carotene, cryptoxanthin, lycopene, selenium and zinc. [Hum Reprod Update. 2017;23(4):371-389.] And omega-3 fatty acids, let's not forget.In human trials conducted on men with fertility problems, fish fatty acid supplementation improves sperm quality. [Andrologia. 2011;43(1):38-47.] [Syst Biol Reprod Med. 2016;62(6):387-395.] [Reprod Biol. 2018;18(3):282-288.]
The Danes studied 1,679 healthy and young men, who signed up for the military between 2012 and 2017. Of these men, 5 percent said that they had taken supplements containing fish oil during the 3 months before their medical check up.

Taking or not using fish oil supplements had no effect on testosterone levels. However, the researchers did find an effect on the production of sperm and the size of the testes. The fish oil users produced more semen and had larger testes than the men who did not use fish oil supplements.

The figures above were made after the researchers statistically brushed out as many other confounding factors as possible.
The testosterone: LH ratio was higher in the men who used fish oil. This could imply that fish oil makes the testes respond better to LH.
The data used for the figure below have been adjusted for confounding factors as much as possible.

LH is a hormone produced by the pituitary gland in the brain. It travels through the blood to the testes, stimulating them to produce more testosterone and sperm cells.Conclusion
"We did not obtain information about the actual content of the omega-3 fatty acids in the supplements, and the study was crosssectional, so we can only claim associations and not causation", write the researchers.

"To our knowledge, randomized clinical trials on intake of fish oil supplements have only been performed among men with infertility, and our findings need to be confirmed in well-designed randomized clinical trials among unselected men or in large prospective cohort studies."
JAMA Network Open. 2020;3(1):e1919462.