In this research manuscript, a new protocol is proposed for predicting the available space in the cloud and verifying the security of stored data. The protocol is utilized for learning the available data, and based on this learning, the available storage space is identified, after which the cloud service providers allow for data storage. The Integrity verification separates the private and the public data, which avoids privacy issues. The integration of the private data is done with the help of cloud service providers with respect to the third-party auditing (TPA). Earlier, public key cryptography and bilinear map technologies have been combined by the researchers, but the computation time and costs were high. To secure the integrity of the data storage, the client should execute several computations. Therefore, this research suggests a reliable and effective method called position-aware Merkle tree (PMT), which is implemented for ensuring data integrity. The proposed system uses a PMT that enables the TPA to perform multiple auditing tasks with high efficiency, less computational cost and computation time. Simulation results clearly shows that the developed PMT method consumed 0.00459 milliseconds of computation time, which is limited when compared to the existing models.