Is a more natural sounding sentence is
A clause having a subject beginning with a preposition is used occasionally.
without the a you will sound non-native.
This sentence is fine:
Does this sentence make any sense?
As per @Subjunctive:
I think this sentence means that a clause has a subject phrase that begins with a preposition
because you are asking about a collection (of types of clauses):
and such types of clauses are used occasionally
Since you are wondering about how to improve your sentence:
I would like a better way rewriting this sentence, please suggest any improvements.
Although what you wrote is understandable:
Please say what you think.
is asking for an opinion, whereas you are asking for suggestions, and again the a:
I want a better way to rewrite the sentence stated above
without which to a native ear will signal you as a non-native speaker