First step, assuming you have only one column in your csv (to understand the complete solution below):
One column
You can use this regex:
sed -r 's/^[^a-zA-Z]*([a-zA-Z]+[^&;]+).*$/\1/' test.csv
Explanations:
-r: use extended regular expressions (avoid parenthesis and plus + symbol escaping)
^[^a-zA-Z]*: skip any non-alpha characters at the beginning, ...
([a-zA-Z]+[^&;]+) ... then captures at least one alpha character followed by a sequence of any character except ampersand & and semi-colon ; ...
.*$ ... and skip any remaining characters (if any, they must begin by either an ampersand or a semi-colon since sed pattern matching is greedy, i.e. it tries to match the longest sequence) until the end of line ...
\1 ... and replace the whole matched text (the line since the regex covers it) by the captured sequence.
Working example:
$ sed -r 's/^[^a-zA-Z]*([a-zA-Z]+[^&;]+).*$/\1/' << 'EOF'
> ABD_1&SC;1233;5665;123445
> 120585_AOP9_AIDMS3&SC;0947;64820;0173
> EOF
ABD_1
AOP9_AIDMS3
Multiple columns:
It looks like you want to process a specific column. If you want to process the n-th column, you can use this regex, which is based on the previous:
sed -r 's/^(([^,]+,){2})[^a-zA-Z]*([a-zA-Z]+[^&;,]+)[^,]*(.*)$/\1\3\4/'
^(([^,]+,){<n-1>}) captures the first (n-1)th columns; replace <n-1> by the real value (0 for the first column works too), and then...
[^a-zA-Z]*([a-zA-Z]+[^&;,]+) captures at least one alpha character followed by a sequence of any character except ampersand &, semi-colon ; or a comma, then ...
[^,]* ... skip any remaining characters which are not a comma ...
(.*)$ ... and captures columns, basically the remaining sequence until the end of line; since any non-comma character was already skipped before, if this sequence exists, it must begin with a comma; finally ...
\1\3\4/ ... replace the whole matched text (the line since the regex covers it) by the following captured sequences:
\1 : the (n-1)th columns (\2 is inside)
\3 : the text we want to keep from the n-th column
\4 : remaining columns if any
Working example (it processes the third column):
$ sed -r 's/^(([^,]+,){2})[^a-zA-Z]*([a-zA-Z]+[^&;,]+)[^,]*(.*)$/\1\3\4/' << 'EOF'
plaf,plafy,ABD_1&SC;1233;5665;123445,plet
trouf,troufi,120585_AOP9_AIDMS3&SC;0947;64820;0173,plot
EOF
plaf,plafy,ABD_1,plet
trouf,troufi,AOP9_AIDMS3,plot