This time in my signature the web site is on free hosting and now i am going to buy a domain and space to establish a new web site my question is that if i change my signature on forums the back links will be considered for new domain it they will be removed for old side and will not effect to my new website
You have to redirect your old domain to the new one (permanent redirection 301) so that your old backlinks will benefit your new site. Otherwise, they are lost.
A new domain name starts over with Google. 301 redirect is what Google recommend, which basically means if you typed in the old the user would be taken to the new domain. You can transfer content, but it will be very difficult to acquire the backlinks. You may be losing all of the backlinks to it
when i join DP when in signature i placed an other and when after some time i came back to DP i change my signature and now links are counted for new one redirection is used for to drive traffic from old to new one i think but not sure let me read google suggesstions carefully any how a new idea are what you say?