1982 yamaha xj6 maxim takes no throttle just bogs

i have had this bike and been restoring it for a good part of a month now
bike is mostly stock has 4 into 2 custom exhaust kn air filter in stock box with lid removed
things ive done to it
- rejetted the main jets to 117.5
-new clutch cable and clutch levers
- rebuilt clutch
im not sure where ive gone wrong it just refuses to take throttle ive got the adjustment screws out three turn new intake boots and carb boots it sounds lean it idles great and will ride with choke no throttle ive synched the carbs not vacuum sync yet

 

As so many others will chime in here..... there are tiny little passages in the carburetor bodies are part of the pilot circuit that transition from the idle circuit to the main jet operation that sound like they are clogged. It only takes a few weeks of lack of use and poor gas for the carbs to clog enough to present the symptoms you describe. The carbs will need to be disassembled and thoroughly cleaned. Search this site for "The Church of Clean". It is not a difficult job but you do need to put the time and effort into the detail work. You will be amazed at how sweet these bikes are when you take the time to get them right.

 

ive run through the church of clean and now it runs and throttles the throttle is inconsistent and has a pop out the exhaust when throttle is let off and is now hard to start when cold

 

Have you sync'd, aka"balanced" the carburetors? How did you adjust the pilot mixture screws under the no tamper caps on the engine side of the carburetors? If you don't have the nice Carb Pro balancing device or are cheap like me you can DIY a device to vacuum balance the carbs with 2 pieces of clear plastic tubing about 6 feet long each. I used a scrap piece of 1 x 3 inch board to hold the tubing in vertical loops and filled them with ATF. Attach the tubing ends to the vacuum ports on the carb boots, #1 and #2 on 1 loop, #3 & #4 on the other and run the engine. Adjust the throttle screws between the carbs until the level of ATF in the loops is even. Then put 1 loop on #2 and #3 and balance them against each other. If they are WAY out it will suck the ATF into the engine and it will smoke like crazy. No worries, it won't hurt anything, just drive the mosquitos away for awhile.
How are you holding the air filter in place without the air box lid? It is part of the air filter hold down assembly and helps seal it to the air box proper. Not having the air box makes carb tuning way more difficult without a great deal of positive return. And having a non-stock exhaust with the air box changes is going to complicate things much further and MAY/probably require jet changes. Most folks here are going to advise against such things. Folks much smarter, experienced, knowledgeable and accomplished than I.
The air screws? Start with them soft bottomed and then screw out 2 to 2 1/2 turns to start. See how that works to get your XJ more cooperative. More folks will be along shortly to comment, without a doubt. Good Luck, this isn't difficult, just sometimes tedious.