You need to escape the backtick, but also escape the backslash:
$ touch 1\` $ /bin/sh -c "ls 1\\\`" 1`
The reason you have to escape it “twice” is because you’re entering this command in an environment (such as a shell script) that interprets the double-quoted string once. It then gets interpreted again by the subshell.
You could also avoid the double-quotes, and thus avoid the first interpretation:
$ /bin/sh -c 'ls 1\`' 1`
Another way is to store the filename in a variable, and use that value:
$ export F='1`' $ printenv F 1` $ /bin/sh -c 'ls $F' # note that /bin/sh interprets $F, not my current shell 1`
And finally, what you tried will work on some shells (I’m using bash, as for the above examples), just apparently not with your shell:
$ /bin/sh -c "ls 1'\`'" 1` $ csh # enter csh, the next line is executed in that environment % /bin/sh -c "ls 1'\`'" Unmatched `.
I strongly suggest you avoid such filenames in the first place.