These can be evidence:
1) in the police:
a copy of the statement about domestic violence;
a copy of the protocol on the commission of an administrative offense;
a copy of the resolution on finding the offender guilty and bringing him to justice, etc.;
2) in a medical institution:
conclusion on the state of health and physical injuries;
prescription for medicine;
referral for treatment;
checks and receipts;
3) in the social service (in case of violence against a child):
a copy of the family/child needs assessment report;
a copy of the report on the results of social support of the family/child;
a copy of the decision to enroll a child in the register of children who are in difficult life circumstances, etc.
Evidence in court can also be:
audio/video recordings of conversations, threats, blackmail;
video of the offender's actions, photos of the consequences of the violence (bruises and scratches on the body);
damaged things;
screenshots of correspondence in social networks;
testimony of witnesses - relatives, neighbors, friends, colleagues, etc.