Minimum duration for presenting a visual stimulus on screen
In psychophysics, this is known as an absolute threshold. The absolute threshold will depend on a variety of factors such as brightness, size, etc.

It is also important to keep in mind that the time needed to detect a stimulus may be too short to cause some desired effect on the participant (e.g. a manipulation). For example, the time needed to detect a stimulus is necessarily shorter than the time needed to identify a stimulus. Though research on subliminal stimuli suggests stimuli can sometimes be presented below threshold and still achieve some manipulation. However, some of this research is controversial.

Often, researchers will choose a range of display times specifically in order to unravel the time course of some cognitive process. For instance, when displaying a cluster of dots, how long is needed in order to subitize them?

There is insufficient information in your question to give you an exact number, but I suggest looking at similar studies and see what sort of display times they use.