HRA

no only one can claim HRA U/s 10(13A)

on only one can claim if paying rent                   

if both are paying Rent of the same house partly then both can claim deduction of HRA

Yes, Why not? If both of them are paying rent and landlord issues either two separate rent receipts or only one receipt specifying the amount or proportion paid by each, then both husband and wife are entitled for HRA exemption according to the amount of rent paid.