A Y90 (Yankee TRACON) Controller reported ALB TRACON does not have communication capability in a portion of ALB airspace. Y90 TRACON does have communication coverage in this airspace. Reporter stated coordination difficulties when aircraft transition this airspace.

Narrative

ZZZ [Center] Sector X initiated an automated handoff of Aircraft X; a VFR aircraft who's destination was ZZZ. The aircraft was flying southwest bound and was right on the boundary line between Y90 and ALB Approach. I utilized the *T function on stars to get a bearing to ZZZ and observed that the line took the aircraft down the boundary line and then would exit Y90 airspace in to the ALB shelf; which they own surface to 5000. Observing this; I initiated an automated handoff with ALB Approach. The aircraft flashed for a minute or two without ALB accepting it so I called on the landline and said 'Albany; Brandley; VFR handoff.' The ALB Controller answered and asked if the aircraft was direct HIDAL; I said no; he's VFR direct ZZZ; to which the ALB Controller replied 'point out approved.' I then expressed to the ALB Controller that this was a handoff because the aircraft would be completely in their airspace once they left the boundary with Y90 and I don't know who is west of that airspace and don't have handoff capabilities with whoever that would be. Since it is known that ALB has very poor radio coverage from the surface to about 4000 in the northwest shelf; I advised ALB I would keep the aircraft until the western boundary and then transfer communications; at which point they said 'radar contact'. As I had coordinated; I did not transfer communications with Aircraft X; and gave a position relief brief in which I communicated this situation to the relieving controller. To my understanding; that controller switched communications at the pre-coordinated boundary. I was informed later that the aircraft then switched back to Y90 frequency to ask for a different frequency as they were unable to make contact with ALB. I was informed 2 days later that ALB had filed an Mandatory Occurence Report saying I had bullied them in to taking a handoff on an aircraft they wouldn't be able to communicate with; even though none of that had been communicated to me by the ALB Controller.I have several recommendations for how this situation could have been handled better; and I will start with what I could have done better. Knowing that a radio issue exists in that area I could have just initiated a point out down the boundary and waited until the aircraft was closer to the western boundary before initiating a handoff; and asked ALB specifically if they would be able to communicate with the aircraft in that airspace; at that altitude. However; I believe there are several contributing factors to this situation that far outweigh anything I did or did not do. To start; the ALB Controller did not express in any way that they wouldn't be able to communicate with the aircraft in that airspace; if they had; I would have done something else to ensure continuous radio communications with the aircraft and air traffic control. Being decisive is part of this job and if you don't understand what someone is trying to coordinate; or what they are trying to coordinate is not possible; it is on you to communicate that. I believe the single greatest contributing factor however is that ALB owns a large chunk of airspace in which they can't communicate with aircraft. In that shelf ALB owns surface to 5000 and to my understanding (even though it is not written anywhere or explained definitively anywhere) they cannot communicate with aircraft below 4000. This seems like a very dangerous situation that is completely preventable by the FAA doing one of several different things. Either that shelf and the underlying airports should be incorporated into Y90 airspace; as we have complete radar and radio coverage there; or the FAA should accommodate the placement of another frequency that ALB can use to ensure radio coverage for their entire airspace. It seems to me that the blame lies on the FAA for this incredibly obvious lapse in safety could be remedied fairly easily; but like many things in the FAA is allowed to just exist until an incident occurs. It seems simple and obvious to me that a facility should be able to communicate via radio frequency to aircraft in their area of jurisdiction; otherwise what is the point of owning that airspace and considering it 'controlled'.