Independent tasks

Is there a possible way to have “independent” tasks in a project?
By independent I mean tasks that do not affect the overall schedule of the project.

The idea is that I would need a resource/task, that by itself is present all the time and it does not affect the scheduling of other tasks, but it is important to include due to project costs. for example server rental or fixed accounting costs. they are paid in a monthly fixed basis and do not affect other tasks because they are a must.
As such I would have the possibility to adjust all other tasks that are dependent and are on a critical path - but not these “independent” tasks.

What I have tried is making a task (with a resource) that starts in the middle of the project and goes all way to the end. but When i try to see the critical path it outlines (obviously) only this task.

Thank you for the help,

@omni-cjlm Have you considered setting date constraints or locking this task to a specific date (like the first of the month?). This is might be the best option if the task has a fixed cost and must simply be represented on the schedule.

Alternatively, you might find setting up a hammock task useful: