Forum tip: telling the reader “it gives me an error” is vastly less helpful than showing the reader the output of trying that:

iex(1)> Jason.decode("{\"custom_key\": \"12\\25\"}")
{:error,
 %Jason.DecodeError{
   data: "{\"custom_key\": \"12\\25\"}",
   position: 19,
   token: nil
 }}

Printing the string involved makes it clearer what’s going on:

iex(2)> s = "{\"custom_key\": \"12\\25\"}"          
"{\"custom_key\": \"12\\25\"}"
iex(3)> IO.puts s
{"custom_key": "12\25"}
:ok

So the JSON parser complains about the lone \ in the input.

In your second example, this happens:

iex(4)> s = "{ \"custom_key\": \"\"12\\\\25\"\"}"
"{ \"custom_key\": \"\"12\\\\25\"\"}"
iex(5)> Jason.decode(s)
{:error,
 %Jason.DecodeError{
   data: "{ \"custom_key\": \"\"12\\\\25\"\"}",
   position: 18,
   token: nil
 }}
iex(6)> IO.puts s
{ "custom_key": ""12\\25""}
:ok

Now the extra "s around 12\\25 throw the whole thing off.

My advice: don’t try to replace values in JSON by string-replacing the whole thing - parse the JSON, do the replacements there, then re-encode.