If it’s the size of a 50p then I think nail varnish won’t get it looking great.
because the paper will have a curved edge, the paint will find it harder to get underneath, thus creating a sort of feather affect.
It works on cars but for bikes it’s a bit more difficult.
Spoil sport.

but yer ok, at that size getting it look good with nail varnish isn't the best solution (good way to get a colour match though).
right, im not on my phone so serious answer.
take the frame to your local car paint place (most towns have one, but only those in the know, know where it is), ask them to colour match it in a rattle can for you, it will cost about 12 quid (which seems expensive for a rattle can, but trust me on this, they are soooooo much better than premade cans you get in halfruads) while you are there pick up a tin of etch primer, this is what makes paint stick to stuff. if it's a steel frame you could probably get away with normally primer.
now, as Mr Master said above, sanding, 600-800 grit maximum, concentrate on the paint edges that are left, you want to smooth those in to the metal so there isn't a massive step (paint is laid on in microns, a thick coat with a clear is abour 180 microns thick, which is just shy of 0.2mm, doesn't sound a lot but anything bigger than around 40 microns will show though the paint).
Mr Masters suggestion for feathering is a good one, we used to do it with masking tape, by only sticking half to the surface then rolling the rest back.
only things missing then are final prep, which is a wipe down to remove grease and dust, not done with the same cloth.
prime it, let it be, prime it again. sand that with 800 grit gentle like then hit the colour, 2-3 layers is enough, they should be sprayed within 20 minutes of each other.
now heres the tricky bit, walk away from it. don't touch it, don't sniff it, don't lick it (never lick it), leave it for 24 hours, preferable somewhere toasty but right now, yer that might not happen.
now you've left it for 24 hours, hit it with a hair dryer. warm that puppy up.
now back to leaving it. when you've left it for a few days, rub it back with 1200 grit to get rid of the orange effect.