FYI, even if OP or someone else doesn't want to run their own full node, they could use service (such as getnodes.io) which offer Bitcoin Core API.
Does this getnodes.io work for you? Can you access the site?
I can't seem to access the site and my AV Kaspersky blocking it I also tried accessing it through other devices but it seems it's down.
Anyway, OP does not look exactly what we pointed to.
i understand your point, sorry i didn't show my intentions more clear. anyways, i want best BTC API to make live bitcoin price tracker for my website.
Now, it's clear well, that the links that I provided are for blockchain development so it won't fit if you are building a live Bitcoin price tracker.
The best API for price tracking is already mentioned above Coingecko and another one is Coinmarketcap but if you still looking for another price tracker with API check this one for Bitcoin only.
https://blockchain.com/api/exchange_rates_api
https://blockchain.com/ticker
https://blockchain.com/tobtc?currency=USD&value=500
http://www.coindesk.com/api/
http://api.coindesk.com/v1/bpi/currentprice.json
http://api.coindesk.com/v1/bpi/currentprice/USD.json