Possible causes –
1) The template which is being applied for this page is having 0 (static or some evaluated result) as prefix to the post content.
2) It’s being added via filtering done by any piece of code in the theme or any plugin through the hook the_content.
3) If the result of each post is being shown via Ajax, then there is chances that exit() or die() is missing at the end of PHP code.
4) Some JavaScript code is prepending 0 to each container of the post content.
Firstly, try with switching the theme, if the issue does not persist, then possibly the issue is occurring via the theme. Revert back to the original theme and check for home page template.
Otherwise, if the issue persists after theme switch, then possibly it’s an issue from any plugin. So try checking for it by activating/deactivating each plugin and then debug further.