Try This
On selected Index Changed Event Of your ddlCity
Dim sd As New SqlDataAdapter("select cityID from tableCity where cityName='" + cmb1.SelectedText.ToString() + "'",connection)
Dim dt As New DataTable
sd.Fill(dt)
If dt.Rows.Count > 0 Then
conn.Open()
Dim cmd1 As New SqlCommand("select BranchNames from tableBranch where cityID='"+dt.Rows (0).Item (0).ToString ()+"'", conn)
Dim dr1 As SqlDataReader
dr1 = cmd.ExecuteReader()
ddlBranch.DataSource = dr1
ddlBranch.DataTextField = "BranchName"
ddlBranch.DataBind()
dr1.Close()
conn.Close()
Implement this as Per Your need.I have taken Field Just For Example.So check it and Try