The Telecare Medical Information System (TMIS) provides a set of different medical services to the patient and medical practitioner. The patients and medical practitioners can easily connect to the services remotely from their own premises. There are several studies carried out to enhance and authenticate smartcard-based remote user authentication protocols for TMIS system. In this article, we propose a set of enhanced and authentic Three Factor (3FA) remote user authentication protocols utilizing a smartphone capability over a dynamic Cloud Computing (CC) environment. A user can access the TMIS services presented in the form of CC services using his smart device e.g. smartphone. Our framework transforms a smartphone to act as a unique and only identity required to access the TMIS system remotely. Methods, Protocols and Authentication techniques are proposed followed by security analysis and a performance analysis with the two recent authentication protocols proposed for the healthcare TMIS system.