Cloud storage systems have been introduced to provide a scalable, secure, reliable, and highly available data storage environment for the organizations and end-users. Therefore, the service provider should grow in a geographical extent. Consequently, extensive storage service provision requires a replication mechanism. Replication imposes many costs on the cloud storage, including the synchronization, communications, storage, etc., costs among the replicas. Moreover, the synchronization process among replicas is a major challenge in cloud storage. Therefore, consistency can be defined as the coordination among the replicas. In this paper, we propose an extension to the strict timed causal consistency by adding the considerations for the monetary costs and the number of violations in the cloud storage systems and call it the extended strict timed causal consistency. Our proposed supports monotonic read, read your write, monotonic write, and write follow read, models by taking into account the causal relations between users' operations, at the client-side. Besides, it supports timed causal at the server-side. We employed the Cassandra cloud database that supports various consistencies such as all, one, quorum, etc. Our method performs better in reducing staleness rate, the severity of violations, and monetary cost in comparison with all, one, quorum, and causal.