120v gfci spa


I have a 120v spa/hot-tub at the main breaker I have 3 wires black/white/ground the ground and white are hooked up at the ground block and the black to a 20 amp breaker.
I have a seperate breaker box with GFCI at the spa 60 amp the gfci has a seperate white jumper on it . 3 wires going to the spa from there. Coming to the Gfci breaker from th main box the black and white are connected to seperate sides of the GFCI aand ground to block. Can I connect the jumper from GFCI to the same blockand also the ground from spa itself. So at the ground block I have main ground, jumper from GFCI and spa ground. At the gfci out to the spa the white wire and the black are hooked where they recieve 120 v I have already done this and the GFCI test works like advertised and the spa also works. Am I protected as I need to be? I was going to run 4 wire but in the main box did not know how to connect for 120 v. Thanks
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You're not making any of this clear. you have a spa that requires 20 amp 120, so why do you have a 60 amp at the spa?

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