i want to create a email subscription page

Try looking for a suitable plugin.

there are many email list plugin, but nothing is suitable for it

where is your email list?

You could make a simple form:
https://www.ads-software.com/extend/plugins/contact-form-7/

To collect the addresses

Then either manually add them to your list, or do something using

https://www.ads-software.com/extend/plugins/contact-form-7-to-database-extension/

Which stores CF7 entries in the DB and allows you to access and do stuff with the data

This would be really useful, especially if it had security feature to prevent automated spammers. Anyone have any suggestions?

the best way to build a mailing list is to have auto responder and there are quite a few on line and they give you html code that you can use to create sign up form.

look for a plugin may be there is one around
I just searched and have not used it try it out see if this works
https://www.ads-software.com/extend/plugins/wp-responder-email-autoresponder-and-newsletter-plugin/