In the study of mean-field-type game (MFTG) theory, understanding how agents interact and make choices in asymmetric information environments has always been a central challenge. Mean-field-type games with asymmetric information explore scenarios where individual decision-makers operate under conditions of partial observation and varying levels of information. This chapter presents MFTGs in which the decision-makers have different information structures and different perceptions of the state process. The observations of the decision-makers are correlated. The payoff functionals involve couplings between the controls of the decision-makers and a covariance between the state and the control action of the decision-maker. The state dynamics is driven by a Gauss-Volterra jump-diffusion process, which includes fractional Brownian motions and multi-fractional Brownian motions. The state dynamics are of conditional McKean-Vlasov type as its coefficients depend on the expected value of the state and the expected value of the control actions conditioned on the switching regime.