Data <- c("Posted by ondrej on 29 Feb 2020."
, "Posted by ona'je on 29feb 2020")

sub(" +?on.*$", "", Data)  # "Posted by ondrej" "Posted by ona'je"
sub(" +?on.*", "", Data)   # "Posted bydrej on 29 Feb 2020." "Posted bya'je on 29feb 2020"
sub(" +?on(.*)", "", Data) # as expected
sub(" +on.*", "", Data)    # as expected