As with a number of Russian Republics, the Republic of Adygea arguably had a semi-presidential constitution for a period.
The current constitution dates back to 1995. A copy in Russian can be found here. They key clauses are the following:
a.) The president is elected for a 5-year term, article 76(3). The president is empowered and steps down prior to the expiration of his term, by and according to the federal law (Article 76(1)).
b.) The president heads the cabinet of ministers and can dismiss it (84.2). The president appoints the PM with the agreement of the Council (legislature) 84.3. The Council has the power of a vote of no confidence (90.1). The president could ask the Council to reconsider, but if it still votes against the PM, deputy PM or any other member of the executive, they have to be dismissed (90.3-4).
This wording seems to be on the cusp of purely individual as opposed to collective responsibility, but Art. 90.1 is probably collective enough for the Republic of Adygea to be considered semi-presidential on the basis of the definition used in this blog.
However, a clarification is overdue. The kind person who translated the Russian text for me also reminded me that the Russian Duma passed a law in December 2004 that abolished presidential elections in Russia’s regions. Instead, they are now appointed by the Federal President. Therefore, any semi-presidentialism in the Republic of Adygea ended with the passage of that law because the president is no longer directly elected.
This point also applies to the previous post on Tatarstan. Apologies for the mistake.