How to arrange datewise data of more than one person when data receive from different date

It's not clear, at least to me, exactly what you want to see as an answer. Please manually add the results you expect to see to the workbook and identify which the results are.

Why do some of the numbers have an asterisk * ?

It means those cells aren't numbers and any solution would be complicated by first having to remove them. Is ths data available WITHOUT *s?

Where does the data come from. Do yuo manually enter it or is it imported from somewhere else?

Is this an import via a hyperlink to a web site URL or data from a csv file which has been output from some back office system?

As I said the addition of the * complicates the task and I'd like to understand whether seeing the original data might offer an easier solution

Using formulas only
Named Ranges:
DateCols =Original!$C$27
DateSpan =New!$A$1:INDEX(New!$1:$1,0,COUNTA(New!$1:$1))
MaxDate =Original!$E$27
MinDate =Original!$D$27
TestRange =INDEX(Original!$A:$A,MATCH("Name",Original!$A:$A,0)):INDEX(Original!$1:$1048576,MATCH("zzzzzz",Original!$A:$A),DateCols)

oldest(or newest) date for per row on original:
D18 (E18):

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oldest (newest) date per report:

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Return a list of names from original to new sheet, column A:

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New sheet date header (B1): (* I did not try to eliminate unused dates*)

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fill dates to the right:

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find data corresponding to date in row one of new sheet in row on original corresponding to name in column A:
B2:

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Result is given in sheet2

In B2 then copied acrooss

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In A3 then copied down

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In B3 then copied across and down
=IFERROR(INDEX(Sheet1!$A$4:$T$12,MATCH($A3,Sheet1!$A$4:$A$12,0),MATCH(B$2,INDEX(Sheet1!$A$4:T$12,MATCH($A3,Sheet1!$A$4:$A$12,0)-1,),0)),"")

Thanks again sir for your quick response.
I have downloaded example1(1)ans.xlsx & when I enter data in sheet 1 as the name of Mark it will automatically update its data in sheet2 but not all data is showing in sheet2. As I enter data in your example1(1)ans.xlsx file in sheet 1.Althouhg previously entered data (which you had enter in sheet1) not completely showing in sheet2. As per data----for Jack data entered for 17 dates but showing 13, for Peter data entered for 16 dates but showing 08, for Mark data entered for 14 dates but showing 10.
Actually I wanted the exactly same data sheet as you provided in sheet2 of example1(1)ans.xlsx. entry data in sheet1 automatically updates data in sheet2. It will be a great help to me if you do it. I uploaded the file which i have enter the data for Mark.

Revised formula in B2 then copied across (Dates). Pl note I have changed Name in A2 in Sheet2 As Names

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You are Welcome. Happy to help.