Hello Damen,
I am really sorry for the delay of this reply as it is actually a long weekend for most of us here (2 separate public holidays on Friday on Monday!) To prevent spammers from posting spam blogs, you need to identify the trusted users on the site which you want to allow postings from and this is what you should do:
1. Once you have identified the users that you trust, assign them into a trusted Joomla user group. It could be "Author", "Administrator", "Editor" or even create a new Joomla user group in Joomla.
2. Then, proceed to the ACL section in EasyBlog and configure the permissions for "Registered" group. Ideally, you shouldn't allow posting permissions from the "Registered" group because by default, when a new user registers on your site, Joomla would assign these users into this group.
3. Then, configure the ACL for the trusted Joomla user group and allow posting and publishing from them.