I am writing this sentence
Patients need to have consultation with doctors.
is it correct to say consultation with doctors or it would be better to say
Patients need to consult an appointment with doctors
You can say:
Patients need to have consultations with doctors.
In this example, consultations is used as a noun.
Patients need to consult an appointment with doctors.
is incorrect because you can't consult (discuss information or advice) with an appointment, which is the object in this sentence. You would have to reorder it a bit:
Patients need an appointment to consult with doctors.
The first sentence sounds correct. Word consultation is regularly used for this purpose.
To consult means:
to ask for information or advice from someone because it is their job to know something
to discuss something with someone so that you can make a decision together
to look for information in a book, map, list etc.
So, you can't really consult an appointment. The 2nd sentence would have to be rephrased to be correct. With the word appointment you can use: make, set, have etc. (have fits your example best, I think).
The first sentence is fine. You may be able to shorten it slightly, since "have a consultation with" is synonymous with "consult", you could say "Patients need to consult a doctor".
Singular "a doctor" probably works better here, but it depends on context, and consider whether "need" or "should" is more appropriate.