Is it possible to stop the consideration of the court case due to the fact that I serve in the army?

NO, it is not possible to stop the proceedings in the case for such reasons, based on the following.

Thus, in accordance with Clause 5, Part 1, Article 236 of the Civil Code of Ukraine, the court stops the proceedings in case of presence of a party or a third person who makes independent claims regarding the subject of the dispute, as part of the Armed Forces of Ukraine or other military formations formed in accordance with the law, which transferred to martial law or involved in the conduct of anti-terrorist operations, - until the termination of the stay of the party or a third person who declares independent claims regarding the subject of the dispute, as part of the Armed Forces of Ukraine or other military formations formed in accordance with the law, transferred to martial law or involved in the conduct anti-terrorist operation.

HOWEVER, as noted by the Supreme Court in its ruling, membership in a voluntary formation does not exempt from the obligation to perform fixed-term military service, military service by conscription during mobilization, for a special period, military service by conscription of officers, military service upon the conscription of reservists in a special period (Clause 6 of the Regulation on the Voluntary Formation of Territorial Communities, approved by the Resolution of the Cabinet of Ministers of Ukraine dated December 29, 2021 No. 1449).

THEREFORE, there are no grounds, in accordance with Clause 5, Part 1 of Article 236 of the Civil Code of Ukraine, to stop the proceedings in the case. In order to stop the proceedings in the case on the above grounds, it is necessary to submit to the court evidence of being in the Armed Forces of Ukraine or other military formations formed in accordance with the law, transferred to martial law or involved in anti-terrorist operations and the performance of combat tasks in the combat zone , which can, first of all, be confirmed by certificates from the place of military service, an order on personnel.