How to move markers (Data Points) of three lines at same category?

What chart type are you using: line or XY scatter? If I had to guess, I would suspect you are using a scatter chart, and the X value for the indicated points (due to round off error or something) is not exactly equal to 48 or 96. Correcting this means looking at the data and determining how to "correct" the X values so that they are exactly equal to 48 and 96.

Your picture looks like a scatter chart, so I am not sure why you did not succeed when you tried a scatter chart. If you give a scatter chart the correct X and Y values, it should plot it just like your picture in post #1. What are you using for the X values for each data series?

In order to plot a point a little to the left (or right) of 48, you must give Excel an X value for that point a little smaller (or larger) than 48. I would expect your data will look something like:

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Then, create a scatter plot where column A and B are for data series 1, column C and D are data series 2, and column E and F are data series 3. You will probably need to use the "Select Data" dialog (Design group) to add the 2nd and 3rd data series.

how can I make the caps of error bars more wider?

The only formatting options that I am aware of are those available in the "format error bars" dialog. You might see what options are available there, but I don't think there is any way to get a wider cap.