How to create single marker on the line chart?

You could add another series with only the required points being plotted.

Post example workbook of you current chart if you need more help.

You are using jargon to describe your problem so I am none the wiser.
What do you mean by simulation or waveform?

If you had posted example as requested maybe those terms would have been more easily understood.

Is this something you can work with? The scroll bar allows you to label any one of the charted points.

So how does my example not meet with your description?

You can use autoshapes or pictures to create custom markers.
Copy the shape, select the series, select the specific data point and Paste.

Here is more detail of custom markers.

Whether you use my suggestions is up to you.

Hi Sir,

I found that the X Value and Y Value under the tab of Data Labels of Chart Option are marked with Green Square instead of tick in your example.
But I could not do so if generate a chart using my own excel.

I'm using Excel 2003

That would suggest that you applied a data label to a single data point.

The green box denotes mixed choices. Some points have a data label others don't.