I've got a Xiaomi Yi camera that uses the same sensor as the Go Pro's from a couple of years ago. I have multiple fence mounting options, including a gorilla pod magnetic tripod for when the field has cloth nets (can tie around a bleacher rail, or stick to the poll holding the net), and a DIY fence mount made of a $3 Chinese selfie stick, a Go Pro hinge mount, and flexible/shapeable rubber twist ties.
I wrap the top of the selfie stick right below the mount with a 6" flexible tie that ends up shaped like a V with hooks on the ends. The hooks suspend the rig to the fence, allowing you to reach overhead with the selfie stick to get a good height on the fence (8'-10') while keeping the camera between the fence links. Then one twist tie secures the selfie stick handle at the bottom so you don't get any movement. Almost have to take a picture of that to make it make sense, but it's a cheap and really secure way to mount it. It might look sketch, but it works surprisingly well.
My whole setup was under $100. I didn't know how much I'd keep up recording games, but when you catch crazy stuff like this crazily umpired play last year that should have had about four outs, it's worth it:
I wrap the top of the selfie stick right below the mount with a 6" flexible tie that ends up shaped like a V with hooks on the ends. The hooks suspend the rig to the fence, allowing you to reach overhead with the selfie stick to get a good height on the fence (8'-10') while keeping the camera between the fence links. Then one twist tie secures the selfie stick handle at the bottom so you don't get any movement. Almost have to take a picture of that to make it make sense, but it's a cheap and really secure way to mount it. It might look sketch, but it works surprisingly well.
My whole setup was under $100. I didn't know how much I'd keep up recording games, but when you catch crazy stuff like this crazily umpired play last year that should have had about four outs, it's worth it: