Anders Gustaf Andersson becomes the stepfather, which may explain why some family trees mention him as the father. But nothing in the records confirms or even suggests that he should have been the biological father.
In Odensvi AI:18 p. 235 one can see that Anders Gustaf was first married (in 1876) to Josefin Elisabeth Blomqvist. They had four children, born 1883-1888. It is of course possible that he should have had an illicit relation with Anna Gustafva in 1884 in the neighbouring parish Munktorp, but there is nothing to confirm it.
Anders Gustaf and Anna Gustafva had a daughter in 1891, before they got married. Anders Gustaf recognised her as his legitimate offspring and this is noted in Odensvi AI:19 p. 232, but no such notes for Anna Gustafvas two illegitimate sons Edvard Johan (b. 1884) and Gunnar Andreas (b. 1889). They both take the surname Andersson, but that's not even circumstantial.