In the Fish shell, how can I join an array with a custom separator?

Since fish 2.3.0 you can use the string builtin:

string join ',' $ASD

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The rest of this answer applies to older versions of fish.

One option is to use variable catenation:

echo -s ,$ASD

This adds an extra comma to the beginning. If you want to remove it, you can use cut:

echo -s ,$ASD | cut -b 2-

For completeness, you can also put it after and use sed:

echo -s $ASD, | sed 's/,$//'