[Answered ]-Can you make an objects that deletes itself in Django?

Just make a filter that prevents retrieving expired VerificationTokens:

from datetime import timedelta
from django.db.models.functions import Now

VerificationToken.objects.filter(
    date_created__gte=Now()-timedelta(minutes=10)
)

You can also make a manager such that VerificationToken.objects is a manager that only contains non-expired tokens:

from datetime import timedelta
from django.conf import settings
from django.db.models.functions import Now

class VerificationTokenManager(models.Manager):
    
    def get_queryset(self):
        return super().get_querset().filter(
            date_created__gte=Now()-timedelta(minutes=10)
        )

class VerificationToken(models.Model):
    user = models.ForeignKey(
        settings.AUTH_USER_MODEL,
        on_delete=models.CASCADE
    )
    code = models.CharField(max_length=4)
    date_created = models.DateTimeField(auto_now_add=True, db_index=True)
    objects = VerificationTokenManager()

you can then make a management command [Django-doc] that you for example run through cron, or some other scheduling task that removes expired VerificationTokens with:

# app_name/management/commands/remove_expired_tokens.py

from datetime import timedelta
from django.core.management.base import BaseCommand
from django.db.models.functions import Now
from app_name.models import VerificationToken

class Command(BaseCommand):
    help = 'Remove expired verification tokens'

    def handle(self, *args, **options):
        VerificationToken._base_manager.filter(
            date_created__lt=Now()-timedelta(minutes=10)
        ).delete()

Note: It is normally better to make use of the settings.AUTH_USER_MODEL [Django-doc] to refer to the user model, than to use the User model [Django-doc] directly. For more information you can see the referencing the User model section of the documentation.