I know that LN is considered as a Off-chain , what about sidechain Pegged may it be also considered Off-chain ? I find many resources on the internet and the opinions do not match. Someone say that it is a off-chain solution but someone consider it as a third possibility : 1) On-chain 2) Off-chain 3) Sidechain
That's probably because there are multiple types of sidechains, each with different effects on scalability.
Federated sidechains have a trusted group of validators that enforces the sidechain consensus. It's basically an altcoin that can interact with Bitcoin. This would be an off-chain solution, since the sidechain consensus doesn't involve Bitcoin miners or mainchain consensus.
Drivechains or merge-mined sidechains are enforced by miners and/or full nodes. While they are not
on-chain in the sense of
the Bitcoin mainchain, they increase mining and full node overheads the same exact way that an on-chain block size increase would.