The aim of this paper is primarily to introduce the quadra Mersenne-Jacobsthal and quadra Mersenne-Pell sequences. Then, the Binet formulas and generating functions for these sequences are obtained. Moreover, quadra Mersenne-Jacobsthal and quadra Mersenne-Pell quaternions were defined and Binet formulas, generating functions, some quaternion sums and relations were obtained for these quaternions.