Trouble shooting home Wireless connection with ISP

I have Xfinity as ISP with cable modem and wireless router. Every time i don’t have internet connection, my setup SSID1 is strong and good. This particular SSID2 is always not there when internet went down. I believed ISP created this SSID2, but they denied it. I have slow connection but when i do speed test it is good. How do I trace and prove my wireless connection is going thru this particular SSID2??