In single-quotes, escapes don't work; they're just a backslash character. The only thing that has a special meaning after a single-quote is another single-quote, and that always marks the end of the single-quoted section. As a result, you cannot embed a single-quote in a single-quoted string.
You have several options. You can end the single-quoted section of the string and use something else to protect the single-quote:
# Single-quoted string, escaped single-quote, then another single-quoted string:
export PASSWORD='vfR"&aDA'\''GzV3(Yg'
# Single-quoted string, double-quoted single-quote, then another single-quoted string:
export PASSWORD='vfR"&aDA'"'"'GzV3(Yg'
Or use a double-quoted string instead (and then escape any double-quotes, backslashes, dollar signs, backquotes, etc that you want in the string):
export PASSWORD="vfR\"&aDA'GzV3(Yg"
Or you could skip quotes entirely and just escape everything individually:
export PASSWORD=vfR\"\&aDA\'GzV3\(Yg