We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy. The conjectures relate the Onsager generators to the conserved charges obtained from semi-cyclic transfer matrices. The conjectures are motivated by two examples which are spin-1/2 XX model and spin-1 U (1)-invariant clock model. A novel construction of the

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... lic transfer matrices of spin-1 Zamolodchikov-Fateev model at arbitrary root of unity value of the anisotropy is carried out via transfer matrix fusion procedure. SciPost Physics Submission B Onsager generators in XX case 17