Direct proof of use
Oryx lists one Russian AShT-4310 topographic command and staff vehicle as destroyed in its running equipment-loss record for the Russian invasion of Ukraine. WarSpotting separately indexes the AShT-4310 among documented Russian material losses in the Russo-Ukrainian war. Together, those loss records place the support vehicle with Russian forces in the 2014 Russia-Ukraine War.
Sources: Oryx Russian Equipment Losses, WarSpotting Russia Loss Search
Narrative
The AShT-4310 entry is a support-equipment case rather than a direct-fire weapon record. The cited Russian listing describes the related AShTTs-4310 as a shelter-body vehicle on a KamAZ-43114 chassis for storing, checking, analyzing, and evaluating terrain information on analog media such as maps and imagery, as well as digital terrain information on CD media.
Its documented conflict role is therefore topographic and staff support: the loss evidence shows the vehicle present with Russia's force structure, while the product listing explains why such a system belonged in a military command-support inventory. The public loss records do not identify a specific unit, location, or dated battlefield incident for the destroyed AShT-4310.
Sources: AShTTs-4310 Product Listing, Oryx Russian Equipment Losses, WarSpotting Russia Loss Search