Hi makumbi,

Refer below sample code.

HTML

<asp:ScriptManager ID="ScriptManager1" runat="server"></asp:ScriptManager>
<asp:UpdatePanel ID="UpdatePanel1" runat="server">
    <ContentTemplate>
        <asp:GridView ID="TeachersCommentsGrd" runat="server" AutoGenerateColumns="False">
            <Columns>
                <asp:TemplateField>
                    <HeaderTemplate>
                        <asp:CheckBox ID="chkAll" runat="server" AutoPostBack="true" />
                    </HeaderTemplate>
                    <ItemTemplate>
                        <asp:CheckBox ID="CheckBox1" runat="server" AutoPostBack="true" Enabled="False" />
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="admno">
                    <ItemTemplate>
                        <asp:TextBox ID="Admno" runat="server" Text='<%# Eval("admno") %>' ReadOnly="True"></asp:TextBox>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="Student Name">
                    <EditItemTemplate>
                        <asp:TextBox ID="TextBox1" runat="server"></asp:TextBox>
                    </EditItemTemplate>
                    <ItemTemplate>
                        <asp:TextBox ID="Names" runat="server" Text='<%# Eval("name") %>' ReadOnly="True"></asp:TextBox>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="Grade">
                    <EditItemTemplate>
                        <asp:TextBox ID="TextBox2" runat="server"></asp:TextBox>
                    </EditItemTemplate>
                    <ItemTemplate>
                        <asp:Label ID="lblCountry" runat="server" Text='<%# Eval("Grade") %>' Visible="False"></asp:Label>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="Grade">
                    <EditItemTemplate>
                        <asp:TextBox ID="TextBox3" runat="server" Text='<%# Bind("Grade") %>'></asp:TextBox>
                    </EditItemTemplate>
                    <ItemTemplate>
                        <asp:Label ID="Label1" runat="server" Text='<%# Bind("Grade") %>'></asp:Label>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="Comments">
                    <ItemTemplate>
                        <asp:TextBox ID="TeacherComments" runat="server"
                            OnTextChanged="TeacherComments_TextChanged" Text='<%# Eval("Remark") %>'
                            CssClass="TeacherComments" onkeyup="enter(this)" AutoPostBack="True"></asp:TextBox>
                    </ItemTemplate>
                </asp:TemplateField>
            </Columns>
        </asp:GridView>
        <asp:HiddenField ID="hfRowIndex" runat="server" />
        <asp:HiddenField ID="hfCellIndex" runat="server" />
    </ContentTemplate>
</asp:UpdatePanel>
<script type="text/javascript">
    function enter(obj) {
        var tr = obj.parentNode.parentNode;
        var cellIndex = obj.parentNode.cellIndex;
        var rowIndex = obj.parentNode.parentNode.rowIndex;
        if (event.keyCode == 37) //Left
        {
            if (cellIndex > 0)
                tr.parentNode.rows[rowIndex].cells[cellIndex - 1].getElementsByTagName('INPUT')[0].focus();
        }
        if (event.keyCode == 38) //Up
        {
            if (rowIndex > 1)
                tr.parentNode.rows[rowIndex - 1].cells[cellIndex].getElementsByTagName('INPUT')[0].focus();
        }
        if (event.keyCode == 39) //Right
        {
            if (cellIndex < tr.cells.length - 1)
                tr.parentNode.rows[rowIndex].cells[cellIndex + 1].getElementsByTagName('INPUT')[0].focus();
        }
        if (event.keyCode == 40) //Down
        {
            if (rowIndex < tr.parentNode.rows.length - 1)
                tr.parentNode.rows[rowIndex + 1].cells[cellIndex].getElementsByTagName('INPUT')[0].focus();
        }
    };

    var prm = Sys.WebForms.PageRequestManager.getInstance();
    if (prm != null) {
        prm.add_endRequest(function (sender, e) {
            if (sender._postBackSettings.panelsToUpdate != null) {
                var rowIndex = parseInt(document.getElementById("hfRowIndex").value);
                var row = document.getElementById("TeachersCommentsGrd").rows[rowIndex + 1];
                if (typeof (row) != "undefined") {
                    var celIndex = parseInt(document.getElementById("hfCellIndex").value);

                    var checkbox = row.cells[0].getElementsByTagName("INPUT");
                    if (!checkbox[0].checked) {
                        checkbox[0].checked = true;
                    }

                    var controls = row.cells[celIndex].getElementsByTagName("INPUT");
                    for (var i = 0; i < controls.length; i++) {
                        switch (controls[i].className) {

                            case "TeacherComments":
                                controls[i].focus();
                                return;

                            default:
                        }
                    }
                }
            }
        });
    }
</script>

Code

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.Add("admno");
        dt.Columns.Add("name");
        dt.Columns.Add("Grade");
        dt.Columns.Add("Remark");
        dt.Rows.Add("1","John","A","Good");
        dt.Rows.Add("2","Suzen","A+","Good");
        TeachersCommentsGrd.DataSource = dt;
        TeachersCommentsGrd.DataBind();
    }
}

protected void TeacherComments_TextChanged(object sender, EventArgs e)
{
    GridViewRow row = (sender as TextBox).NamingContainer as GridViewRow;
    int kk = row.RowIndex;
    //(TeachersCommentsGrd.Rows[kk].Cells[1].FindControl("checkbox1") as CheckBox).Checked = true;

    hfRowIndex.Value = row.RowIndex.ToString();
    hfCellIndex.Value = "5";
}

VB.Net

Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs)
    If Not Me.IsPostBack Then
        Dim dt As DataTable = New DataTable()
        dt.Columns.Add("admno")
        dt.Columns.Add("name")
        dt.Columns.Add("Grade")
        dt.Columns.Add("Remark")
        dt.Rows.Add("1", "John", "A", "Good")
        dt.Rows.Add("2", "Suzen", "A+", "Good")
        TeachersCommentsGrd.DataSource = dt
        TeachersCommentsGrd.DataBind()
    End If
End Sub

Protected Sub TeacherComments_TextChanged(ByVal sender As Object, ByVal e As EventArgs)
    Dim row As GridViewRow = TryCast((TryCast(sender, TextBox)).NamingContainer, GridViewRow)
    Dim kk As Integer = row.RowIndex
    hfRowIndex.Value = row.RowIndex.ToString()
    hfCellIndex.Value = "5"
End Sub

Screenshot