General aviation instructor pilot reported a near miss in the traffic pattern at a non-towered airport in daylight visual conditions during a training flight. The instructor identified the other aircraft performing a non-standard entry into the traffic pattern and maneuvered abruptly to avoid a possible collision; then landed safely.

Narrative

Day 0 at ZZZ (uncontrolled airport):XA:10: PIC (pilot in command) in C172 Aircraft X announces on CTAF intentions to departs ZZZ Runway XX for left closed traffic on XX.XA:11: Aircraft X takes Runway XX and departs for left closed traffic.XA:12: Aircraft X is at pattern altitude and on left crosswind. Aircraft X announces on CTAF he's turning left downwind XX.XA:12: Aircraft Y announces on CTAF he's crossing mid-field for tear-drop entry into left downwind XX.XA:13: Aircraft X notices on 'ADS-B IN' that Aircraft Y is on a potential collision course. Aircraft X asks the traffic on midfield what altitude he's crossing midfield. Aircraft Y replies he's crossing mid-field at pattern altitude.XA:13: Aircraft X visually identifies Aircraft Y off left wing and on a potential collision course. Takes evasive action to avoid impact. XA:15: Aircraft Y lands and taxi's for fuel. While there a CFI witnessed the event and re-affirmed midfield crossings must occur >=500 ft. above pattern altitude. Also noted the pilot in Aircraft Y is a known hazardous pilot who CFI's refuse to fly with because of such attitudes.Summary:While flying left closed traffic on Runway XX in ZZZ (uncontrolled); Aircraft Y crossed midfield at pattern altitude (rules state midfield crossing occur >=500 ft. above pattern altitude) and almost caused a collision. After learning this is not a student; but rather a private pilot with known hazardous attitudes and a history of cutting pilots off in the pattern; I decided best action would be to report the event so corrective action could be addressed and future risk could be mitigated.