This app was mentioned in 8 comments, with an average of 1.63 upvotes
He has Notification Reminder (Quick): https://play.google.com/store/apps/details?id=com.bhanu.notificationreminders
For me the best is Recurrence (https://play.google.com/store/apps/details?id=com.bleyl.recurrence)
I use this: https://play.google.com/store/apps/details?id=com.bhanu.notificationreminders&hl=en Notification Reminders. Set a quick note and it pops onto your status bar and pull down notification shade as if its a text message.
Now reading better, I see what you need, an Android notification that cant be deleted! Well, Todoist do not have anything like that as far I know, but could be a great idea to Devs!
Try an app called "Notification Reminder" https://play.google.com/store/apps/details?id=com.bhanu.notificationreminders&hl=pt-br
More of a reminder app, but is this the sort of thing you're looking for?
Not the exact thing OP asked for, but this comes way closer.
https://play.google.com/store/apps/details?id=com.bhanu.notificationreminders
I use this: https://play.google.com/store/apps/details?id=com.bhanu.notificationreminders&hl=en_GB
Notification reminder. Nice and simple and works great.
Direct link : https://play.google.com/store/apps/details?id=com.bhanu.notificationreminders
Looks great, downloading it now.