Velvet is a very contagious parasite and annoying to get rid of... I am going through it now myself with Phoenix... he's had it for several weeks and I had no knowing of it until yesterday, my daughter who is 13 years old decided not to tell me several weeks ago that he had stopped eating.
Needless to say I had an explosion over her mistreatment of him... it's a long story so I'll cut it short... he was left untreated for 3 weeks in total, again I had NO knowing of this until yesterday, researched and went and bought Nox-Ich... it's a very strong parasite medication that removes a lot of parasites from the betta fish.
You'll know your betta fish is losing them when you find little odd particles at the top of the aquarium floating about in the water, scoop these out right away, could take a day or two before you start seeing them.
He has been in quarantine himself... if your betta has a fine gold/rust mist to his/her body.. it's likely to be velvet... treat it asap... if it gets tobe serious like Phoenix's is you will be in for a very long battle.
I done the following for my betta fish... I removed ALL gravel and tossed it in the trash (best to buy new, not taking chances with the old, it may contain the parasites and I don't want it back), I done a full 100% water change because Phoenix's tank is only 3 gallons, I used aquarium salt, a pinch of Epsom salt.
I removed and disinfect ALL items/decorations from the aquarium/tank and put in a pale or big bucket of bleach and hot water, wash, rinse very well then air dried, this includes extra bowls fish is placed in, nets, toys, etc...
Make sure to disinfect the heater in the bleach and water solution (I used 1/2 cup bleach in a big pale), rinse heater very very well and place back in the aquarium because the fish will only need a heater and a home to hide in inside the aquarium.
I then placed Phoenix in a completely different container (that I threw away later on) after his transfer from aquarium to container and back to aquarium.
I then used Lysol anti-bacterial kitchen cleaner and sprayed his whole aquarium, used a separate soft sponge and cleaned it all over, rinsed very well, then stuck it in vinegar for 5 minutes, rinsed very well, stuck it in bleach for 5 minutes, rinsed very well, dried it with a clean rag towel to throw away later.
I refilled his aquarium with bottled water, aquarium salt and Epsom salt, used his water conditioner and then I put in the dosage of his medication in his aquarium before I put him back in 10 minutes later.
Nox-Ich is the brand I used for my betta fish... it's a little more harsh than any other brand but it works... my betta fish is JUST starting to come around again, if you want quicker results this will work but it's 1 drop per gallon. If you want more details send me a message and I'll send you a picture... best of luck to you and your betta, I wish the little darling a get well soon and a very quick recovery, :)