CE700 First Officer reported incorrect entry in the FMS resulted in a TAWS alert and a CFTT event.

Narrative

Day five; third leg; 12 hrs into duty day; night flight from ZZZ1 to ZZZ. I was the pilot flying (PF) in the right seat. Inbound to ZZZ we reviewed both runways and the visual guided maneuvers pages. Once we knew ZZZ was landing runway XX the pilot monitoring (PM) in the left seat inputted the runway XX visual guidance track into the standby flight plan which I reviewed. Northwest of the field the controller cleared us the visual XX and we proceeded direct ZZZZZ; 1547 ft runway touchdown zone was entered in the altitude alerter; we configured before ZZZZZ; got on speed; and captured the VNAV glidepath. Everything was normal. I noticed we were descending a bit aggressively; we were closer to the ground than anticipated; and I got that uncomfortable feeling. The TAWS system announced 'too low; terrain'. I immediately disconnected the autopilot and initiated a climb to pick up a normal glideslope to land on Runway XX uneventfully. In the chocks we checked the FMS points and VNAV inputs and found we had inadvertently programmed the 1547 ft touchdown zone and 4 degree glide path at point ZZZZZ1. I put this down to a late day for me; night flying; over reliance on the FMS and VNAV; and especially not doing a thorough CAMI (Confirm; Activate; Monitor and Intervene) check of the guided visual track inputs. Suggestions: One barrier to this scenario is to rename point ZZZZZ1 a different name to avoid mixups.