I would just get a better Power Supply with a new GPU. If you are willing to spend the cash on a GTX 1060 then for around the same price you could chuck in a RX 480 and new Power Supply and as they say
"kill 2 birds with one stone". But if it's too much even an RX 470 and new Power Supply would be better than just a 1050 Ti or trying to push your low-tier Power Supply to the limits with a GTX 1060. Here is a partlist for reference:
PCPartPicker part list:
https://pcpartpicker.com/list/3TtyZ8
Price breakdown by merchant: https://pcpartpicker.com/list/3TtyZ8/by_merchant/
Video Card: Gigabyte Radeon RX 480 4GB G1 Gaming Video Card ($199.49 @ OutletPC)
Power Supply: SeaSonic S12II 520W 80+ Bronze Certified ATX Power Supply ($48.99 @ NCIX US)
Total: $248.48
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-04-16 11:59 EDT-0400
If it is too much swap the RX 480 for a cheaper RX 470 and it should be borderline $200 or so. I would advise against pushing that Power supply especially if you have had it for a few years already, the last thing you need is for it to die and risk taking other components with it, it wouldn't be the first time this happened on a VS PSU or any other low-tier one for that matter. Hope this helps