I am using Sony a6500 but I have Godox V860 ii C and Godox X1T C trigger. Can I use this flash and trigger on my Sony camera for high-speed sync? Will it work? If yes, how to do it?
If you need TTL/HSS, then whatever goes on the hotshoe of the camera has to have a matching flash foot that has all the contacts required for electronic communication. So, the V860II-C or the X1T-C will not work with full function on the Sony multi-interface hotshoe of the α6500. Only the -S versions will. With the -C versions, you will get triggering, and probably M power control if the X1T is placed into single-pin mode (Fn 01 = on). But HSS, if you meant high-speed sync, and not tail-syncing (aka hi-sync, hypersync, supersync, overclock sync, etc.) is probably not going to work.
You can, however, use the V860II-C as an off-camera TTL/HSS/remote power control radio slave to an X1T-S (or, better yet an XPro-S or R2 Pro II-S), so long as its firmware is at v1.4 or later. (See also: How do I tell if my Godox trigger or flash needs a firmware update?)
TL;DR: You might need to update the firmware in the V860II, and purchase an additional and correct trigger.
To use all the flash modes and features, your a6500 will require the X1T-S version of the trigger. In the same vein, the V860II-C cannot fully work when directly mounted on the Sony a6500 hot-shoe. You will need the V860II-S version for that.
In case you want to be fully compatible at low cost, the V8600II-C will work seamlessly with a X1T-S trigger on your a6500 (ttl, hss and all).
Working with your current gear
The only mode that will work with your current gear is the "single contact mode". You will need to set the Godox X1T-C to single contact mode (Fn1=on, see the X1T-C user manual page 38) and pair it with V860II-C in manual mode. Set the Sony a6500 to fill flash (see online manual here).
Flash power can then be adjusted manually on the X1T-C (or on the V860II-C for that matter). Of course, you won't have any automatic feature working. But at least, it will flash.