Suffixes in an author name such as 'Jr', 'Sr' and 'IV' do not need to be included in-text, though you will need to include the suffix in the reference list.
Jones, H. W., Jr., & Jones, H. W., Sr. (1941). My adventures in Alexandretta.
The Journal of Fictional Archeology, 1, 1–19. https://doi.org/46.34262/56637
Note: Titles, positions, ranks or academic achievements in author names (e.g. Minister, Prime Minister, Governor-General, PhD) are NOT included with the author name in the in-text citation or reference list entry