How long must tax preparers keep paper copies and supporting documents of client returns?

See if this info from IRS is helpful

https://www.irs.gov/businesses/small-businesses-self-employed/how-long-should-i-keep-records

"One website said 7 years"

This is more of a Practice Advice question. You would understand that record retention for the professional preparer is not the same as for the taxpayer. You provided a service to them in the line of your authority to file on their behalf, so your responsibilities are different than the taxpayer's personal responsibility. You might like to read this:

https://www.aicpa-cima.com/resources/article/document-retention-faqs-for-tax-practitioners

In general, you want to have whatever your client might need for as long as a client might need it. Beyond that, you need to provide for your own professional needs.

For the most part, it is three years for Federal income tax returns (States vary) and four years for payroll.

However, it is interesting that "three years" isn't what you may expect, and could be closer to four years.  Below is an excerpt of an article that mentions the weird timing, as well as some other interesting information about how long we need to keep records (and some thoughts about keeping them longer).

"The return copies or the list must be maintained for three years after the close of the return period (as defined in Sec. 6060(c)). Unfortunately, the term “return period” as defined for this section is most likely not the period that most practitioners would anticipate. Rather, it is the 12-month period beginning on July 1 of each year and is unrelated to the tax return period or the tax return deadline.

For example, a tax preparer prepares and delivers an individual 2022 return in August 2023. The “return period” per the Sec. 6060(c) definition ends on June 30, 2024, so a copy of the return (or the list) would need to be maintained until June 30, 2027."

https://www.thetaxadviser.com/issues/2023/feb/documentation-and-recordkeeping-for-tax-practitioners.html

Some states have their own rules that need to be followed.  NY preparers are 7 years.