When i put my bike into gear it just shuts off

I have the 1100 diagram and it is either the fuseable link/in-fuse just after the positive or the fuses on the starter relay.
Service manual here;
https://data2.manualslib.com/pdf5/106/10596/1059519-suzuki/gsx600f.pdf?819c1462fc9f65eb841adda066024bf1

try a can of Seafoam $10 @Autozone our in 1/3 to 2 gallons gas and drive for about 10 to 15 miles and see if that stuff will clean out the whole fuel injector and idle system get on it once in awhile to but be safe. Now if that doesnt do it, then look for loose hoses or vacuum leaks...just spray carb cleaner around the throttle body and injectors and if the idle increases you've found your leak. i hope this was at least helpful Thanks!

It has injectors.Does it display any "C" codes when you crank it up? Did you ever tinker any Fuel Injection modules or sensors? Have you inspected/ or visual checked or try to replaced your fuel filter?

Check fuel filter and drain carb bowls. It sounds like water or debris, shutting you down.

check the kick stand switch...it sounds like it sticking out....so even when you put the kick stand up the switch is stuck out....so the engine wil cut out as it thinks kick stand is still down....give it a spray with wd40...or something like ....but work it till it no longer sticks.......

Sounds like your clutch is stuck on [not disengaging when you pull the leaver]This can happen over a long storage-no use period.To fix put the bike in 3rd gear and start the engine with the clutch lever pressed[caution the bike will want to surge forward so keep your foot on the brake]Make shure to have the engine up to normal running temperature before you try this fix.the engine firing along with the brake pulled will release the sticking clutch plates.This will work!!!

Some bikes have a kickstand safty switch on them if your kickstand is down the bike will shut off in gear.

hi mate adjust the clutch cable when you put it into gears the clutch is still grabbing so it needs to be adjusted

Sounds to me to be something to do with the neutral switch. It stops you starting the bike when it's in gear and you havnt got the clutch pulled in. I'd check along those lines.