Canoonet.eu has given a list of phrasal verbs, but I cannot really find the correct usage of most of these verbs. What is the correct usage of abängsten?
Both verbs were used synonymously in the past but abängsten is no longer used and abängstigen only rarely used in modern German.
Both were reflexively used similar to sich ängstigen but with the prefix ab- to further strengthen the meaning. An English translation for sich abängstigen could be
to be overly frightened of sth., to be overly scared for so. (coll. to be uberscared)
The word is archaic, so correct current usage is not to use it at all. Nevertheless you can find it in a dictionary with the example
Jettchen ängstigte sich um ihn Stunde um Stunde ab.