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For high mobility communication scenario, the recently emerged orthogonal time frequency space (OTFS) modulation introduces a new delay-Doppler domain signal space, and can provide better communication performance than traditional orthogonal frequency division multiplexing system. This article focuses on the joint channel estimation and data detection (JCEDD) for hybrid reconfigurable intelligent surface (HRIS) aided millimeter wave (mmWave) OTFS systems. Firstly, a new transmission structure is designed. Within the pilot durations of the designed structure, partial HRIS elements are alternatively activated. The time domain channel model is then exhibited. Secondly, the received signal model for both the HRIS over time domain and the base station over delay-Doppler domain are studied. Thirdly, by utilizing channel parameters acquired at the HRIS, an HRIS beamforming design strategy is proposed. For the OTFS transmission, we propose a JCEDD scheme over delay-Doppler domain. In this scheme, message passing (MP) algorithm is designed to simultaneously obtain the equivalent channel gain and the data symbols. On the other hand, the channel parameters, i.e., the Doppler shift, the channel sparsity, and the channel variance, are updated through expectation-maximization (EM) algorithm. By iteratively executing the MP and EM algorithm, both the channel and the unknown data symbols can be accurately acquired. Finally, simulation results are provided to validate the effectiveness of our proposed JCEDD scheme.