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x is a quotation I found/read on the internet.

I'd leave out the "quoted by someone", because the fact that an anonymous user also happened to cite this quotation - that this person was not the original source - is of no consequence to either the interpretation of the quote nor the person you're citing it to.

Moreover, when you say "I found a quote", it implies that it was presented to you in that form, that is, as a quote.
Otherwise you could say "I'm quoting something (a sentence, a paragraph, &c.) I found on the internet".

Grammatically it is almost completely fine, but I would use 'happened', since this occurred in the past and does not occur at this very moment:

"A quote, quoted by someone that I happened to read on the internet"

In addition, as FumbleFingers mentions in a comment, the double use of quote is not very appealing. You can use 'cite' as an alternative for the verb 'quote', or 'citation' for the noun 'quote'.

Nevertheless, I'd leave out the "quoted by someone", because the fact that an anonymous user also happened to cite this quotation - and that this person was thus not the original source - is of no consequence to either the interpretation of the quote nor the person you're citing it to:

x is a quotation I found/read on the internet.

Moreover, when you say "I found a quote", it implies that it was presented to you in that form — that is, as a quote.
Otherwise you could say "I'm quoting something (a sentence, a paragraph, &c.) I found on the internet".

x is a quotation I found/read on the internet.

I'd leave out the "quoted by someone", because the fact that an anonymous user also happened to cite this quotation - that this person was not the original source - is of no consequence to either the interpretation of the quote nor the person your citing it to.

Moreover, when you say "I found a quote", it implies that it was presented to you in that form, that is, as a quote.
Otherwise you could say "I'm quoting something (a sentence, a paragraph, &c.) I found on the internet".

x is a quotation I found/read on the internet.

I'd leave out the "quoted by someone", because the fact that an anonymous user also happened to cite this quotation - that this person was not the original source - is of no consequence to either the interpretation of the quote nor the person you're citing it to.

Moreover, when you say "I found a quote", it implies that it was presented to you in that form, that is, as a quote.
Otherwise you could say "I'm quoting something (a sentence, a paragraph, &c.) I found on the internet".

x is a quotation I found/read on the internet.

I'd leave out the "quoted by someone", because the fact that an anonymous user also happened to cite this quotation - that this person was not the original source - is of no consequence to either the interpretation of the quote nor the person your citing it to.

x is a quotation I found/read on the internet.

I'd leave out the "quoted by someone", because the fact that an anonymous user also happened to cite this quotation - that this person was not the original source - is of no consequence to either the interpretation of the quote nor the person your citing it to.

Moreover, when you say "I found a quote", it implies that it was presented to you in that form, that is, as a quote.
Otherwise you could say "I'm quoting something (a sentence, a paragraph, &c.) I found on the internet".