Father's claim on my mother's property

Yes, your father is entitled to equal share in the property along with you and your sister.

Thanks for replying.. If a part is given to him. Does he have right to write a will to any body else, other than me and my sister.

In the case of a female dying intestate section 15 comes into operation,   which is reproduced below :

15. General rules of succession in the case of female Hindus.
          (1) The property of a female Hindu dying intestate shall devolve according to the    
          rules set out in section 16;
          (a) Firstly, upon the sons and daughters (including the children of any pre-deceased    
           son or daughter) and the husband;
          (b) Secondly, upon the heirs of the husband;
          (c) Thirdly, upon the mother and father;
           (d) Fourthly, upon the heirs of the father; and
          (e) Lastly, upon the heirs of the mother.
           (2) Notwithstanding anything contained in sub-section (1),
          (a) Any property inherited by a female Hindu from her father or mother shall
          devolve, in the absence of any son or daughter of the deceased (including the
          children of any pre-deceased son or daughter) not upon the other heirs referred to   
          in sub-section (1) in the order specified therein, but upon the heirs of the father;   
          and
         (b) Any property inherited by a female Hindu from her husband or from her father-  
         in-law shall devolve, in the absence of any son or daughter of the deceased   
         (including the children of any pre-deceased son or daughter) not upon the other   
         heirs referred to in sub-section (1) in the order specified therein, and upon the heirs
         of the husband.

 Yes, he has the right to gift/donate his share to anyone of his choice through a will or any other mode.

Dear Mr.Rajesh,

yes, he has every right to convey the property  in any manner  for his share.

Sir , i want to confirm that  the father does not have the self aquired property which he has got the share from his wife's property so,will that share also  can be given to any one apart from his children?

yes

it is open to your father he can convey the said property at his choice even other than the children