But, I will like to know if there can be any way someone can check the validity of his paper wallet private key correponding to his address. I am thinking of Iamcoleman, but it is possible to use such to test the validity?
You cannot check individual private keys with iancoleman. OP can either use bitaddress.org, click on "Wallet Details", and paste the private key in there, or could use
https://brainwalletx.github.io/, click on "Private Key", then "Toggle Key", and paste the private key in there. Since bitaddress only generates legacy addresses, then either should work. Note that of course you should never paste a private key in to a live website, as you are highly likely to have your coins stolen. If using either of these sites, make sure you download them from the GitHub and run in an airgapped environment.
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I tried simply saving the bitaddress.org page, and it still generated keys correctly for me. The most likely culprit here is OP's wallet is generating a P2SH or P2WPKH address instead of a P2PKH, or he has used the wrong one of the compressed/uncompressed key.