How do I add the paymentAmt based on the CaseId

And for an expression rule you could use this.

a!queryEntity(
  entity: cons!DATA_STORE_ENTITY,
  query: a!query(
    aggregation: a!queryAggregation(
      aggregationcolumns: {
        a!queryAggregationColumn(
          field: "caseId",
          isgrouping: true
        ),
        a!queryAggregationColumn(
          field: "paymentAmt",
          isgrouping: false,
          aggregationfunction: "SUM"
        )
      }
    ),
    filter: a!queryFilter(
      field: "directDepositTF",
      operator: "=",
      value: true /*Or "1"??*/
    ),
    pagingInfo: a!pagingInfo(1, - 1)
  )
)

//How do I put this in Appian:

SELECT [caseId]
,[directDepositTF]
,[deptCaseTypeId]
      ,[caseTypeCode]
      ,[paymentFormTypeId]
,SUM([paymentAmt]) AS aggPaymentAmt
FROM [Appian_DB].[dbo].[CSO_PAYMENT_FILE_OUTPUT_VIEW]
WHERE directDepositTF = '1' AND paymentFormTypeId = '1' and recptDateTS >CONVERT(VARCHAR(10),GETDATE(),110) and recptDateTS < CONVERT(VARCHAR(10),GETDATE()+1,110)
GROUP BY [caseId],[directDepositTF],[deptCaseTypeId],[caseTypeCode],[paymentFormTypeId]

//How do I put this in Appian:

SELECT [caseId]
,[directDepositTF]
,[deptCaseTypeId]
      ,[caseTypeCode]
      ,[paymentFormTypeId]
,SUM([paymentAmt]) AS aggPaymentAmt
FROM [Appian_DB].[dbo].[CSO_PAYMENT_FILE_OUTPUT_VIEW]
WHERE directDepositTF = '1' AND paymentFormTypeId = '1' and recptDateTS >CONVERT(VARCHAR(10),GETDATE(),110) and recptDateTS < CONVERT(VARCHAR(10),GETDATE()+1,110)
GROUP BY [caseId],[directDepositTF],[deptCaseTypeId],[caseTypeCode],[paymentFormTypeId]

Or Maybe a Query Rule can do this?

You would have the view in the database and then query that view through a query rule.