Hi I have my public address and my recovery phrase how do I create my private key for the public Bitcoin address.
As long as you have the recovery phrase, you can recover it on whichever software you generated the seeds on.
If you forgot the software or service that generated your seeds then you will have to quickly use the most trusted seed recovery service (such as blockchain.info or electrum) and after you recover the seed, immediately generate a new address or wallet and send all your coin to that address to avoid getting your coin stolen unless you planning to use that most trusted software.
Never have anyone to manually recover for you or use the untrusted source as your coin may immediately get stolen before they give you the key.
The normal recovery procedure would be to download the latest version of the wallet software you originally used onto a new clean computer and give it the recovery phrase at startup - the exact details depend on what software you used.
If the wallet software is no longer supported or not available you would have to use different wallet software that supports the same seed-phrase system.
Most wallets support a seed-phrase system known as BIP-39.
The popular Electrum wallet uses its own system but I think it may have some capability for importing a BIP-39 seed-phrase.
You can probably tell which is used by looking at the relevant word-list for BIP-39.
When using the seed phrase with a different wallet, you also need to make sure it uses the same derivation path. Wallets have a default derivation path and some let you specifiy a specific derivation path when first started up. Details depend on the exact software used.
Some third-party businesses offer both wallets and accounts. These are effectively non-custodial and custodial wallets. The recovery process may be tied to a specific business. I would avoid trusting such businesses but many people seem to find them convenient. At least until they suddenly go out of business!
If you have a blockchain.info recovery phrase (not from an old backup), then you have enough with your recovery phrase. You can enter it here and create your new account.
In other wallets, this can also be the case. So the rule is, if your recovery phrase is some where between 12-15 English words, you actually have the Mnemonic_phrase and can recover it in a lot of wallets (Electrum, Blockchain, ...)
For other type of recovery phrase, we need to know the wallet software you are using. Because they use the name 'recovery phrase' for something non-standard.