Is there any later version of Bitcoin address generation, than 1? I'm looking for the technical details regarding the format and generation of Bitcoin addresses. I've found this article, “Technical background of version 1 Bitcoin addresses”, on the Bitcoin wiki, but as the title says, it's version 1. It seems to be not talking about the version prefix used in generation of Bitcoin addresses.

Is there any later version of it, the method of the generation, such as version 2 Bitcoin addresses?
Yes, there are P2SH addresses, specified in BIP13. They were introduced in 2012 together with the P2SH consensus rule change. They use Base58 version number 5, and are mostly used for multisig constructions (where multiple parties/devices need to sign off on a transaction).

Recently Bech32 addresses were proposed in BIP173, to enable sending to native SegWit addresses. These addresses are easier to read/write, more compact in QR codes, and have better error detection properties. Native SegWit outputs are cheaper to spend and offer a higher security level (disclaimer: I authored BIP173).