Can 'Candidature-Ship' be proper word . or it must be just Candidature ! Like , I would like to apply my candidature -ship for the post Retail Manager . Is the sentence is Valid ?
Don’t use either in the way you propose.
For clarification, the state or condition of being a candidate is “candidature” or “candidacy”.
But you’re not applying to be a candidate for the job, you’re applying to be hired for the job. So I think you’d want to say:
I would like to apply for the Retail Manager position.
The term is candidateship but it is actually very rare;
(Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.)
The more commonly used term is candidacy as shown in Google Books.
In the context you are suggesting you are applying for job/position and you might say, for instance:
“I hope my candidacy/application receives favourable consideration"