Vitamin D

RCT: Vitamin D supplementation raises testosterone in "healthy" overweight men.
https://www.ncbi.nlm.nih.gov/pubmed/21154195
Participants: Healthy overweight men undergoing a weight reduction program.
Dose: 3,332 IU vitamin D daily
Duration: 1 year
Impact in Vitamin D levels: Mean circulating 25(OH)D concentrations increased significantly by 53.5 nmol/l in the vitamin D group, but remained almost constant in the placebo group.
Impact on testosterone: Compared to baseline values, a significant increase in total testosterone levels (from 10.7 ± 3.9 nmol/l to 13.4 ± 4.7 nmol/l; p < 0.001), bioactive testosterone (from 5.21 ± 1.87 nmol/l to 6.25 ± 2.01 nmol/l; p = 0.001), and free testosterone levels (from 0.222 ± 0.080 nmol/l to 0.267 ± 0.087 nmol/l; p = 0.001) were observed in the vitamin D supplemented group. By contrast, there was no significant change in any testosterone measure in the placebo group.

Observational study: Vitamin D positively correlated with testosterone in older men
https://www.ncbi.nlm.nih.gov/pubmed/26610790

Observational study: Vitamin D NOT correlated with testosterone in men!
https://www.ncbi.nlm.nih.gov/pubmed/28041602
We observed no significant association of 25(OH)D with total testosterone in men

Observational study: Vitamin D is associated with hypogonadism in Chinese men
https://www.ncbi.nlm.nih.gov/pubmed/26177638