Finding the Min value for a subgroup, filtering out preceding Min values within the same parent group

Quite a hard problem. Here is a recursive solution:

WITH 
  rcte AS
  ( SELECT TOP (1)
        Acc, TranType, posCancelID,
        CAST('=' + CAST(posCancelID AS VARCHAR(20)) + '=' AS VARCHAR(MAX)) AS IDs 
    FROM
        MCancel
    ORDER BY
        Acc, TranType, posCancelID

    UNION ALL

    SELECT
        Acc, TranType, posCancelID,
        CAST(IDs + CAST(posCancelID AS VARCHAR(20)) + '=' AS VARCHAR(MAX))
    FROM 
      ( SELECT
            m.*, 
            r.IDs, 
            ROW_NUMBER() OVER (ORDER BY m.Acc, m. TranType, m.PosCancelID) AS rn
        FROM
            rcte AS r 
            JOIN MCancel AS m
                ON  (m.Acc = r.Acc AND m.TranType > r.TranType)
                OR  (m.Acc > r.Acc)
        WHERE
            r.IDs NOT LIKE ('%=' + CAST(m.posCancelID AS VARCHAR(20)) + '=%')
      ) AS mc
    WHERE
        rn = 1
  )
SELECT Acc, TranType, posCancelID
FROM rcte
ORDER BY Acc, TranType ;

The solution assumes that a posCancelID should not appear twice in the result set. If the requirements are that they should not appear twice in the same Acc group, then the solution needs a slight adjustment:

---

WITH rcte AS
  ( SELECT 
      Acc, TranType, posCancelID,
      CAST('=' + CAST(posCancelID AS VARCHAR(20)) + '=' AS VARCHAR(MAX)) AS IDs 
    FROM
      ( SELECT 
          Acc, TranType, posCancelID,
          ROW_NUMBER() OVER (PARTITION BY Acc ORDER BY TranType, PosCancelID) AS rnk
        FROM MCancel
      ) AS f
    WHERE rnk = 1

    UNION ALL

    SELECT
      Acc, TranType, posCancelID,
      CAST(IDs + CAST(posCancelID AS VARCHAR(20)) + '=' AS VARCHAR(MAX))
    FROM
      ( SELECT
          m.*, r.IDs, 
          ROW_NUMBER() OVER (PARTITION BY m.Acc
                             ORDER BY m.TranType, m.PosCancelID) AS rn
        FROM
          rcte AS r 
          JOIN MCancel AS m
              ON  (m.Acc = r.Acc AND m.TranType > r.TranType)
        WHERE
          r.IDs NOT LIKE ('%=' + CAST(m.posCancelID AS VARCHAR(20)) + '=%')
      ) AS mc
    WHERE rn = 1
  )
SELECT Acc, TranType, posCancelID
FROM rcte
ORDER BY Acc, TranType ;

Both are tested at dbfiddle.uk

Using a CURSOR:

This solution uses a temporary table to store each calculation of minim value and filtering next one using data stored in this temporary table for the previous Acc values.

CREATE TABLE #tmp
(
    Acc int, 
    TranType int, 
    PosCancelID int
);
GO

DECLARE @acc int, 
        @trantype int, 
        @poscancelid int;

DECLARE cur CURSOR FOR
    SELECT   Acc, TranType
    FROM     MCancel
    GROUP BY Acc, TranType
    ORDER BY Acc, TranType;

OPEN cur;
FETCH NEXT FROM cur INTO @acc, @trantype;

WHILE @@FETCH_STATUS = 0  
BEGIN

   INSERT INTO #tmp
   SELECT Acc, TranType, MIN(PosCancelID)
   FROM   MCancel
   WHERE  Acc = @acc
          AND TranType = @trantype
          -- filter any previous min value for same Acc
          AND PosCancelID NOT IN (SELECT PosCancelID 
                                  FROM #tmp
                                  WHERE Acc = MCancel.Acc)

   GROUP BY Acc, TranType;

   FETCH NEXT FROM cur INTO @acc, @trantype;

END 

CLOSE cur;
DEALLOCATE cur;

SELECT * FROM #tmp;

Acc | TranType | PosCancelID
--: | -------: | ----------:
100 |        1 |           2
808 |        1 |           4
808 |        2 |           5
813 |        2 |           3

db<>fiddle here