So how a President can be elected among the opposition if the Parliament votes on his person and it's not up to popular election?
I don't know in what other countries Presidents are picked by the legislative body, but we can take a look at Hungary.
But a caveat: here the President is weak, so to speak, the authority, the power of the position is narrow, more like a figurehead, a symbol of national unity and such. Not sure how would play out to elect a President with strong powers by the parliament. The US has this weird electorate system, which is basically a combination or rather a compromise between popular and legislative votes.

First thing first, a shortlist of our Presidents:
Göncz Árpád - 1990-1995, 1995-2000
Mádl Ferenc - 2000-2005
Sólyom László - 2005-2010
Schmitt Pál - 2010-2012
Kövér László - 2012-2012 - was for a month, acting temporarily, more later at his part.
Áder János - 2012-2017, 2017-2022(?)