I have applied for a position last month and the deadline is on March. But by this time one of my work has been published in a good journal (which I wrote in my CV as under review). The position is competitive. Is it ok if I mail the professor and ask him to read my published work? (Though the published work is not so much similar to his work). Will it add extra value to my application? (I have talked with the professor regarding his work and admission several times through email)
I think it is fine to send the article, but not even necessary to ask him/her to read it. It is enough just to make it available, with a note about where it is published. It will be read or not, whether you ask or not. It is also good whether it is closely related to the professors area of research or not.
But making it available easily is a good thing to do and should enhance the application. It shows something about your ability, even if the sub-field is different and even if it isn't read.
MAR is the deadline for applying or for the decision? (Action to take is similar with perhaps a minor different flavor.)
A. If for the application, just send an updated CV and a short note why (the paper accepted).
B. If for the decision, than send an email letting them know the paper was accepted and that you are still interested in the position. Short and sweet email. More of just a touch point since you have an excuse to do so.
P.s. In either case, do NOT bother attaching the paper--you didn't attach the in review papers, why attach the in press ones?