Can my grand child claim a share in my wealth

Your grand child has a share in your intestate property by law of inheritance.

It cannot be claimed as a matter of right during your life-time.

No, during your lifetime  your grand child can not claim any share and right over your self acquired property. 

If  this is your self acquired property then even your son or spouse cannot claim any share in it  as a right, you can deny their claim and can decide about transferring the same as per your will and wish to any person of your choice, you do not have to be under pressue or budge to any emotional or sentimental blackmail too.

It is your earned property your grandchild cannot claim rights over the property.

The question is whether the grandchild has a share in the property not whether the grandchild can claim a share in the property. It means a share in intestate property. If a person dies intestate his grandchild will have no share in the property so long as the son or daughter through whom he or she is grandchild, is alive. If the son or daughter of the person dies before the person then the respective grandchild/grandchildren will have right on the property which would have been the share of their dead parent. It makes no difference whether the property was self-acquired or inherited.  In films and TV serials grandson or son makes claim and ask for division of the property especially ancestral property from the grandfather/father who is alive.

You may appreciate the fact that grandchild is begotten from your son/daughter, who would be class 1 heir after your life, when you did not execute any testamantory document to dispose off your self-acquired property.

The facts posted involve complex legal issues, which are disjointed and not clear to form proper opinion and oblige.

The answer is No, 

Your grandchildren have no right over your self acquired property..You can bequeath the property as per your wish and will..

Why often the word self-acquired property is used? Whether inherited property or self-acquired property the law is the same so long as the deceased had a clear independant tiltle over the property.