General aviation pilot reported a near miss with another aircraft during initial climb from a non-towered airport in VMC. The pilot maneuvered to remain clear of the other aircraft.

Narrative

I just departed Runway 01 at 6B0; making a left midfield downwind departure to the south in my Aircraft X; and I made a call on CTAF stating precisely that. Immediately after my CTAF call; conflicting Aircraft Y made a call on CTAF stating something to the effect that he was 'from the south at 4;500 MSL would be overhead the airport at traffic pattern altitude.' I thought that seemed aggressive considering his proximity (very near) to the airport; and it would require him to make a very high rate of decent.' I noticed on my TCAD/ADS-B that we had conflicting courses (his target showed a direction vector) and that he was descending; so I stopped my climb at 3;300 MSL. He continued his descent and direction into me. He was never making any effort to deconflict; despite the apparent conflict on our ADS-Bs (he was ADS-equipped). I made another call on CTAF; querying what he was doing. He was showing that he was at my 1 to 2 o'clock position; with no visual separation; because of this; I couldn't turn right to deconflict (exacerbate the problem) and could not descend as he was descending AND verbally indicated that he was trying to get to pattern altitude (1;500' MSL). I also couldn't turn left because of the terrain (mountains).The pilot of Aircraft Y did nothing to deconflict from a very near collision. Instead; he aggravated this dangerous situation with both erroneous CTAF calls and his incorrect entry into the airport environment. This pilot; in my opinion; should be immediately re-examined on his knowledge of traffic deconflictions and uncontrolled airport traffic patterns. Based on this incident; it is clear that he is a liability to others and himself.