For truly "vintage" editions (from the 80s or 90s), the Internet Archive (archive.org) is a goldmine. Community members often upload scanned PDFs of historical magazines.
If you remember the story but not the issue date, search for the author’s name followed by "Swathi Weekly Serial." swathi weekly magazine old editions link
Most popular Swathi serials were eventually published as standalone novels. Searching for the book title is often easier than finding the original weekly magazine links. Why Links for Old Editions are Rare For truly "vintage" editions (from the 80s or
Iconic novels by writers like Yandamoori Veerendranath. swathi weekly magazine old editions link
Websites dedicated to preserving Telugu literature often have sections for periodicals.