Don't quote quotes. Go to the original publication and quote from there. Only if that is not available to you (which is rarely believable with almost everything being available online or through interlibrary loan) may you quote from a secondary source.
If you quote a quote or paraphrase, quote it verbatim. The footnote is not part of the text, so don't insert it there. How you handle the quote depends on what exactly you are citing.
Let's assume what you have lying on your desk is an article by Miller (2018), which quotes a book by Johnson (1873). Johnson's argument is that the barn was on fire; Miller's argument is that he ran away (but did not see the fire, so he quotes Johnson to explain that part of the events).
a. If you want to discuss Johnson's claim that the barn was on fire, you would do something like:
Johnson (1873; quoted from Miller, 2013) claimed that the barn was on fire.
You cannot give a direct quote, because that is not given in Miller's article, so you have to paraphrase. If there was a direct quote from Johnson in Miller, your quote of it would look something like this:
"The barn is on fire." (Johnson, 1873; quoted from Miller, 2013)
b. If you want to discuss Miller's running away (irrelevant of wether or not there was a fire) you would either paraphrase it:
Miller (2013) ran away.
Or quote it directly:
"The barn was on fire1 so I ran away." (Miller, 2013)
In both cases (a and b) you do not cite the footnote, nor give the reference in your bibliography, because you are not concerned with the fire, only with the running away.
It may help you to imagine your thesis as an argument. Are you arguing with Miller or with Johnson? Quote the text of the author that you are "talking to". Quote it verbatim, including in-text references as they are printed. Handle them like typos (which you must not correct, either!)
The most basic rule is that you can only cite texts that you have read! You cannot cite what others have read. The simple reason is that Miller might misrepresent Johnson. Maybe "the barn is on fire" does not mean in the context of Johnson's argumentation how Miller uses it in his own.
Examples of exceptions are: lost texts that have only survived in quotes and must be reconstructed from there (e.g. ancient philosophers), or valuable manuscripts that have not been digitized and can only be accessed by travelling to a foreign country (e.g. an unpublished collection of letters). In all other cases you must get the original text and read that. Of course a bachelor's thesis is not a doctoral dissertation, so you will not spend lots of money on acquiring literature, and you may not have the time to wait the weeks that some international interlibrary loans take, but make a decent effort and at least grab a copy of every digital source that you can access.
I'm quoting APA style because I'm more familiar with that, but what I discuss here is indepentent of the style you use. Simply adapt my examples to your style guide.