My road bike tire is damaged because of some biketrap I fell into. After a month I got a flat while riding. I found this hole at the damaged area while repairing the puncture on inner tube. After pumping some air the inner tube is popped out from this hole. I put folded piece of paper inside to prevent another flat until I get home but I dont think that will hang on a bit more. Any longtime solution to last it longer would be helpful.
You may be surprised how long your paper patch lasts. I've used dollar bills, empty energy gel packs and they have lasted quite a long time, but now carry Park Tool Tire Boots.
They have an adhesive and attach to the inside of your tire and stay put, even if you get another flat and have to change tubes. I've found that the money or paper solution will move or fall out of place without the pressure of the tube to hold it in place.
You should be able find the Park Tool Tire Boots at any local bike shop, but here is a link to Amazon: Park Tool TB-2 Emergency Tire Boot
I always carry a spare inner tube AND a cheap small tire patch kit, plus 2 CO2 cartridges with me when I ride. That way, in theory, I can fix up to two flats on a ride. The tire patch kits go bad over time, so I replace them regularly.
In practice, I have used the time patch kit to repair tire cuts much more often than I use it to fix a second flat. The patch stays in place regardless of tire pressure, prevents road dirt from working its way through the tire (into the space between tire and tube- where it can cause another flat), and can help stop rips or cuts from spreading.
I have fixed tires this way and forgotten about the fix, riding 300 - 500 miles before remembering that I needed a new tire. It's pretty effective and has some advantages over the dollar bill fix. Plus you can use it to fix a tube! But remember you still need a new tire.
The dollar bill trick is good for getting home, but eventually the linen fibers will wear out.
You can make your own tire boots by scrounging a tubular tire. Cut out a 7cm by 3cm rounded rectangle, and peal off the tread if you can. I found one in the trash at a local bike store three decades ago and I've only used a small portion of it.
To glue it in place, find some contact cement that has the word FLAMABLE on it, because then you know that it has solvents that will soften the surface rubber.
This will probably sound crazy, but I sewed up a tear in the sidewall with fishing line once. Lasted six months at least, running at full pressure on my daily commute (7 miles round trip). If I had made my seam about 1/4 inch longer than the tear on each end of the tear, it would've lasted even longer.
Just be sure you're threading into the unfrayed portion of the tire's fabric. And this obviously would only work on the sidewall, if at all.