Equivalent of the term "apocryphal", but for quotes?

attributed (adj.)

Given as an attribute or appropriate possession; ascribed as proper to.

1854 (title) Edward III: a Play attributed to Shakespeare. (OED)

attribute (v.)

Ascribe a work or remark to (a particular author, artist, or speaker)

The building was attributed to Inigo Jones Lexico

misattribute (v.)

Wrongly attribute.

The professor misattributed Robert Burn's famous line to Shakespeare. Lexico

It is well-established that many of the most famous quotes are not accurate...In 2012, Quentin Schultze and Randall Bytwerk demonstrated that a quote attributed to Joseph Goebbels, beginning "If you tell a lie big enough and keep repeating it, people will eventually come to believe it', then found on over half a million pages of the internet, was never said by him. They used the term 'referential credibility' for when a quotation is believed by the community using it to have been correctly attributed to a person important to that community. Helen King; Hippocrates Now (2019)

They run a website for young people about books they like to read. This site, Inside a Dog (named from a quote attributed to Groucho Marx, 'Outside of a dog, a book is a man's best friend. Inside a dog, it's too dark to read') is 'all about books, by young people for young people'... Andrew Goodwyn et. al; The Future of English Teaching Worldwide (2018)

He was fond of the phrase “The coldest winter I ever spent was August in San Francisco”—an adaptation of a quote misattributed to Mark Twain —and used it to temper the glow of his happiness when sending notes to his colleagues out east. Susannah Cahalan; The Great Pretender (2019)

Apocryphal works just fine for quotes. From the OED (see statement):

apocryphal, adj. and n.

A. adj. Of doubtful authenticity; spurious, fictitious, false; fabulous, mythical.
a. originally of a writing, statement, or story.
_{Source: Oxford English Dictionary (login required)}

Why, here are a few apocryphal quotes now!

Let them eat cake! — Marie Antoinette

That’s one small step for man, one giant leap for mankind. — Neil Armstrong

The end justifies the means — Machiavelli

Be the change that you wish to see in the world — Gandhi

Et tu, Brute? — Julius Caesar

If the bees disappeared off the surface of the globe then man would only have four years of life left — Albert Einstein

_{Source: Unveiling History’s Apocryphal quotes, or when we render to Caesar things that aren’t his at all}

Seen about:

By the time Russert was working for then-Gov. Mario Cuomo in 1984, the New Yorker carried a possibly apocryphal quote from presidential candidate Gary Hart — “Get me a Russert!” — that fueled the operative’s legend.
_{Source: Washington Post via East Bay Times — Media reeling from Russert’s death}

One especially famous, if possibly apocryphal, quote that has been attributed to everyone from Frank Zappa to Elvis Costello to Thelonious Monk, pertains to the art of music criticism. It runs: “Writing about music is like —

dancing about architecture”

_{Quiz source: The Guardian — From Marilyn to Shakespeare: how well do you know history’s most bungled quotes?}

A possibly apocryphal quote attributed to Mario Vargas Llosa puts it well: “Life is a shitstorm, in which Art is our only umbrella.”
_{Source: Literary Hub — Literature for This Long, Dark Night of America’s Soul}