does bitcoin-core support bip44 HD wallet If bitcoin-core does not support bip-44, is there any other node ?
No, Bitcoin Core uses the BIP32 derivation path m/0'/0', and you are unable to change the derivation path of the wallet in Bitcoin Core.     

There is however the Hardware Wallet Interface (HWI) that might be what you are looking for.      

https://github.com/bitcoin-core/HWI
https://github.com/bitcoin-core/HWI/blob/master/docs/bitcoin-core-usage.md