I am analyzing a Binary dance in 3/4 time by J.C.F. Fischer for an exam in L9 Harmony Royal Conservatory. The start key is F major. Modulates briefly to B flat major and C major. Then a chord A major leads to D minor. What key is here with C sharp , B natural E natural and F natural ? The overall key is F major . The accidentals are C sharp and B natural.
No common, standard key signature contains that combination of notes. The only key signature with a single sharp is G major / E minor with an F sharp. All other keys signatures with sharps will also contain F sharp.
However, that combination of notes will be common in a piece in D minor. The key signature of D minor is the same as that of F major and has one flat which is B. A melodic minor scale will raise the 6th and 7th notes by a semitone when ascending. So, in the key of D minor, the B flat would become a B natural and the C natural would become a C sharp. When descending, these changes don't happen and the B remains flat and the C remains natural. The usage in a melody will be more complicated and up to the composer but it will be common that the 6th and 7th will be raised sometimes and not others. This will not usually be done by changing the key signature but with accidentals.
So, for the question in the title: no (common) key signature contains those notes.
For the question at the end of the body of the question: if the key signature is one flat but many accidentals are used to give B natural and C sharp then it is probably D minor rather than F major.
I say "common" since I don't want to assert that no one uses weird key signatures with oddities such as a F natural and a C sharp.
There is also the possibility of modes being involved but in the simple world of just major and minor keys then you are probably looking at D minor.
This is why I suggest learning the fifths method of music theory. It can't be major because every key that has C# also has F# since accidentals 'carry over' to the key a fifth higher.
And if it can't be major then it also can't be natural minor as each major has a corresponding natural minor.
So you're left with other minors such as harmonic and melodic which Tim has already answered in a comment as D melodic.
I just wanted to explain the methodology.
The start key is F major.
That would be a key signature of one flat.
But your descriptions hints at the possibility of
D minor. In modern key signatures that would also be one flat, but for the Baroque period of Fischer that would be a so-called Dorian key signature and list zero sharps or flats.
Modulates briefly to B flat major and C major.
That would be accomplished with accidentals
B flat major and
B natural for
C major. Those are accidentals used internally modifying the initial key signature. Sometimes a key signature will be changed within the piece rather than using accidentals, but this isn't always the case. I wouldn't expect that in this particular piece. Key signature changes inside a piece tend to be to distant keys where using lots of accidentals is inconvenient and difficult to read.
Then a chord A major leads to D minor.
If the initial key is actually
F major, you can call this a secondary dominant and label it for analysis like this:
F: I... V/vi.... The ellipses are just to indicate the harmony continues in some way. The slash
/ denotes a secondary relationship.
What key is here with C sharp , B natural E natural and F natural ? The overall key is F major . The accidentals are C sharp and B natural.
This part of your question isn't clear. Use of accidentals within the piece doesn't mean you have to change key signatures. At the passage where an
A major chord goes to a
D minor chord there probably are accidentals
B natural. That would make sense for minor mode harmony, but you can probably just analyze it as a secondary relationship. If the passage is such that it sounds like a bona fide cadence in
D minor label the entire passage with
Dm: and analyze according to that key.
If this is an exam, surely these analysis methods were part of your course.
You should better study the minor scales and the relative keys before analyzing this task:
In music theory, the term minor scale refers to three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just one as with the major scale.
The melodic minor scale has the same upper tetrachord like it's parallel scale: in a-minor this is E,F#,G#,A and in d-minor the notes you are mentioning: A,B,C#.D.
Your piece of Fischer begins probably in Dm (i), Bb (VI), C (VII), A (V), D (i). (Mind that Bb and C are also IV - V in F major - the relative key of d-minor.)
F major (or the key of F) is a major scale based on F, with the pitches F, G, A, B♭, C, D, and E. Its key signature has one flat: B♭. Its relative minor is D minor and its parallel minor is F minor.
To confirm you can look up the compositions of Fischer in IMSLP. I've downloaded yesterday the Suites for trumpets by Fischer, there is a Suite in D-minor. (maybe this is your piece).