Mysidia Adoptables v1.3.1[Security Release]

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Nope it will not mess up with things, your only problem appears to be the missing field from table prefix.users.

To accomplish this task, you need to go to the tab 'Structure' in Phpmyadmin. Now look at the screenshots below. The first one tells you how to add new field(note you must add the new field after the field 'password'!), the second one gives more detail on what values you should enter when phpmyadmin asks you to add a new field.