Hello x34cha,
Overall, I think you may need to provide some additional information: e.g., make and model of routers, access points, etc. that you are using.... The solution may require some configuration change(s).
Why two networks with the same ssid? Not a criticism - just curious about the bigger picture.
Anyway as I understand it, bssids involve MAC addresses. Maybe somewhere within your network devices you may be able to establish the desired block using MAC's. Either a direct block targeting a specific MAC address or limiting access to an allowable list of MAC's.
To be honest I am a bit out of my comfort zone here. However, I think some additional information will facilitate finding any potential solutions. Thanks...