Can my 3-month-old child get some kind of status or certificate, if so

Yes, one can get the status of a family member of a deceased (deceased) Defender.

According to Art. 10-1 of the Law of Ukraine "On the Status of War Veterans, Guarantees of Their Social Protection", the families of fallen (deceased) Defenders of Ukraine include families of servicemen (reservists, conscripts, volunteers of the Territorial Defense Forces) of the Armed Forces of Ukraine who defended independence , sovereignty and territorial integrity of Ukraine and took a direct part in the anti-terrorist operation, ensuring its conduct, being directly in the areas of the anti-terrorist operation during its conduct, in the implementation of measures to ensure national security and defense, repel and deter the armed aggression of the Russian Federation in Donetsk and Luhansk regions, ensuring their implementation, being directly in the districts and during the implementation of the specified measures, in the measures necessary to ensure the defense of Ukraine, the protection of the safety of the population and the interests of the state in connection with the military aggression of the Russian Federation against Ukraine and died (missing), died as a result of injury, contusion, mutilation or disease received during direct participation in an anti-terrorist operation, ensuring its implementation, being directly in the areas of an anti-terrorist operation during its implementation, during direct participation in the implementation of measures to ensure national security and defense, repulse and deterring the armed aggression of the Russian Federation in the Donetsk and Luhansk regions, in ensuring their implementation, being directly in the areas and during the implementation of the specified measures, during direct participation in the measures necessary to ensure the defense of Ukraine, the protection of the safety of the population and the interests of the state in connection with the military aggression of the Russian Federation against Ukraine.