There are many people that say we shouldnt even say his actual name but where does it come from to call him yashkah padrik.
Apparently, it's a long-standing tradition handed down orally that the Roman soldier who raped Mary was called Panderik. So I've been told. Caveat Emptor.
Yoshke is a diminutive of J.
For an online source see the bottom of this page which claims:
Yoshke Panderik (יאָשקע פּאַנדריק) or Yoshke Pandre (יאָשקע פּאַנדרע). A book called "Toldot Yeshua" claimed that his father was actually a Roman soldier named "Pandeira," whose identity was hidden by Mary. See also: http://forward.com/culture/160737/yoshke-of-nazareth/
The link quoted has other ideas. Yoshke is not really diminutive but nomatricon (abbreviation) of Yimakh shemo יִמַּח שְׁמוֹ "May his name be obliterated" is a curse the name of particular enemies of the Jewish people. Note that the full phrase ימח שמו וזכרו has the abbreviation ישו which is also the transliteration of the name used for that person.
The Wikipedia article on (ישו (יהדות refers to ישו בן פנדירא [Yeshu ben Pandeiro] as a possible name for Jesus of Nazareth in uncensored editions of a Tosephta in Maseches Chulin.
I suggest this as a source for the the names “yashkah padrik” and similar.