Please advise if it is a sin for asking his share of inherited property of father, when mother is alive and she doesn't want to distribute it in her life.
The shares of inheritance are accrued at the time of death. That means the inheritors own their shares when the person dies. Your mother is now holding your property without your approval. This is an unlawful act. There is no sin in asking for your property or even applying to judicial authorities for it.
It is recommended that you show the verses below to your mother and ask for your shares on inheritance.
Allah the Almighty commands:
“Allah gives you the task (of inheritance) concerning your children: one share of the male will be equal to two shares of female. If there are more than two daughters, they shall split two-thirds of the inheritance evenly. If there is only one daughter, she shall have half of the inheritance. If the deceased has any offspring, each of his parents shall have a sixth of the inheritance. If the deceased has no child and his parents alone inherit him, then one-third shall go to his mother. If the deceased has siblings, then one-sixth shall go to his mother. All these shares are to be distributed after any task given from it (as a payment) or any written debt is paid. You do not know which of them, your parents or your children, are more beneficial to you. The shares are determined by Allah, for He is All-Knowing, and He judges rightly. To you belongs half of whatever has been left behind by your wives if they die childless. If they have (at least one) child then to you belongs a fourth of what they have left behind, after any task given from it (as a payment) or any written debt is paid. To them belongs a fourth of what you leave behind if you die childless. If you have (at least one) child then to them belongs one-eighth of what you have left behind, after any task given from it (as a payment) or any written debt is paid. If a man or a woman has no surviving heirs such as parents or children but has a half-brother or a half-sister from the mother side, then each of these shall inherit one-sixth. If they are more than two, then they shall split one-third of the inheritance evenly, after any task given from it (as a payment) or any written debt is paid, without incurring a detriment. This is a task (given to you) from Allah. Allah is All-Knowing, the Indulgent. These are bounds set by Allah. Allah will let the ones who obey Allah and His Messenger, enter gardens beneath which rivers flow. There, they will settle for good. That is the great triumph. Whoever disobeys Allah and His Messenger and transgresses the bounds set by Him, Allah will cause him to enter a fire, and there, he will settle for good. He will have a humiliating punishment.”(An-Nisa/The Women 4:11-14)