Both versions are used,but according to Google Books yada is more commonly used than yadda:
This phrase is a modern-day equivalent of 'blah, blah, blah' (which is early 20th century). It is American an emerged during or just after the Second World War. It was preceded by various alternative forms - 'yatata, yatata', 'yaddega, yaddega' etc. The earliest of these that I have found is from an advertisement in an August 1948 edition of the Long Beach Independent:
- yada yada"Yatata ... yatata ... the talk is all about Chatterbox, Knox's own little Tomboy Cap with the young, young
All of those versions, and including 'yada yada', probably took the lead from existing words meaning incessant talk - yatter, jabber, chatter.
'Yada yada' itself is first found in the 1970s.
In the 21st century the place you are most likely to come across it is when installing software; for example, the millions who have installed the Google Toolbar will have seen (although probably not read any further than) the instructions - "Please read this carefully - It's not just the usual yada yada."
(The Phrase Finder)
yadda yadda yadda
Used to indicate that further details are predictable or contextually evident from what has preceded.
‘boy meets girl, boy loses girl, yadda yadda yadda’
1940s: imitative of meaningless chatter.