You can create  a site  stapling feature and write a small code to set the
masterpage to the current master  page. Search for site branding on google.

The site  Master page  only applies to publishing  sites. You need to set the
System Master page to the one you want to use to have that applied to your
non-publishing sites.

First, You would need to identify the type of site. Is your site  a
publishing or non-publishing site. If you recall, in the interface of
the browser you actually have two setting  that allows you to manipulate
the settings  associated with the master  page.

Second, I am making some assumptions here, you would need to ensure that
the inheritance of the master page  has not been changed. That means
that a site owner has not chosen to specify their own master page at a
specific site.

Generally when the Site Master Page settings are changed and forced to
the lower level sites, your newly created  site will use the new master
page settings for all newly created publishing  sites. That is due to
the publishing features. In other words, the newly created publishing
sub-site points to the Master Page Gallery hosted by the Top Level site.

On the other hand, configuring the System Master Page settings and
reseting that configuration for the lower level sites  only affect
sub-sites that are created. After creating a sub-site that doesn't use
the publishing features, it uses the master page (default.master) in its
local Master Page Gallery. That behavior is by design. In the event
you want to change that behavior, you will need to programmatically
make that change.

I have gone through some other solution like " I am going to
Save that site  as sitetemplate and
whenever i am creating a new site I will Chose that Custom Template then I
am able to Inheriting the MasterPage for new Subsites"

Do you have Publishing and Publishing Infrastructure features turned on?
Inheritance of masterpages only works if Publishing is enabled.