What methods are available to search for “lost or abandoned “ bitcoin?
There are no methods available to other people (third parties). People could search for dormant amounts that were outputs of old transactions and not yet used as inputs to subsequent transactions - but those amounts may not actually be lost or abandoned. There is no way to recover control or gain control of these amounts without additional information known only to the person who received those amounts of bitcoin.
If you previously received some amount of bitcoin into a bitcoin wallet, you can search for evidence - perhaps a note of an online website who stored that amount on your behalf and who you could now contact for assistance. Perhaps some old "wallet.dat" files on a PC that indicate you had a desktop wallet with control of your own private keys. Maybe an app on an old phone in a drawer. Perhaps a written down recovery seed or private key in a locked box you use for important documents.
If you do not control the private keys to the addresses where you received your bitcoins, there is no way to recover it. However, if you were using a third party service that were holding your bitcoins for you, you can enquire with their customer service department – Ugam Kamat – 2019-06-20T16:58:11.983