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In this paper, we classified ergodic maximal $u$-entropy measures among theset of partially hyperbolic diffeomorphisms with $(E^{uu},A)$-Markov partition,$c$-mostly contracting center and $c$-mostly expanding center in the$C^1$-topology. More specifically, ergodic maximal $u$-entropy measures can bedivided into $c$-$u$-states and $c$-$cu$-states. Due to the existence of$c$-mostly expanding center, ergodic maximal $u$-entropy measures of type$c$-$u$-states are trivial. For ergodic maximal $u$-entropy measures of type$c$-$cu$-states, by noting that its structure is similar to that of physicalmeasures, with the help of the skeleton we obtain their properties of supportsand basins, and variation of number in some sense. Consequently, the ergodicmeasures of maximal $u$-entropy of type $c$-$cu$-states are finite in the sensethat the measure supports are consistent. On the certain environment, union ofthe basins of ergodic measures of maximal $u$-entropy of type $c$-$cu$-statesis dense in whole space and number of $c$-$cu$-state is upper semicontinuous inthe sense of support.  Finally, we provide propositions for qualitative construction examples, whichalso explains that there are many such examples here.

Geometrical and maximal u-entropy measure-theoretic structures of maps with c-mostly expanding center and c-mostly contracting