How can I add alphanumeric, numeric and email validate validation in my custom form?
You can use Form API Validation module for this.

It has Available Validators like "alpha_numeric" which accept only Alpha Numeric characters and for more see below image.



Just install the module and enable it in admin and then

For alphanumeric use:

'#rules' =&gt; array('alpha_numeric'),


For numeric use:

'#rules' =&gt; array('numeric'),


For email use:

'#rules' =&gt; array('email'),