What are the landlord's rights if a tenant has not paid a the security deposit for a rental but is still claiming ownership of..

If you have already turned over possession of the property it would be unwise to attempt to deny access without consulting an attorney on the specific details. this could leave you open to liability. However if they have not paid rent under the terms of the lease it is very likely you could begin the eviction process to have them removed. If they are paying rent but have not provided the deposit it is likely that you could count the rents paid as deposit first and then claim they have not paid the rent under the terms of the contract, but again I would consult a local attorney on the details before taking action.