Syntax error in select statement C#

String selectStr = "select * from " + thisTable + " where pId = " + argID + "  OR   pAltId = " + alt_ID +" OR  pMobile = " + p_mobile +" OR pDate =" + p_date +" OR 
pName = '"+ p_Name +"'"

Something better to use would be

SqlDataReader selectCommandResult = null;
try{
SqlCommand selectCommand = new SqlCommand("SELECT * FROM @table WHERE pId = @paramId OR pAltId = @paramAltId OR pMobile = @paramMobile OR pDate = @paramDate OR pName = @paramName", SqlConnectionHolder) { CommandType = CommandType.Text };
selectCommand.Parameters.AddWithValue("@table", thisTable);
selectCommand.Parameters.AddWithValue("@paramId", argID);
selectCommand.Parameters.AddWithValue("@paramAltId", alt_ID);
selectCommand.Parameters.AddWithValue("@paramMobile", p_mobile);
selectCommand.Parameters.AddWithValue("@paramDate", p_date);
selectCommand.Parameters.AddWithValue("@paramName", p_Name);

selectCommandResult = selectCommand.ExecuteReader();
                var returnValue = "0";
//You should state what columns you wish to returns instead of using wild cards as table structures can change
                while (selectCommandResult.Read())
                {
                    columnOne = selectCommandResult.GetValue(0).ToString().Trim();
                    columnTwo = selectCommandResult.GetValue(1).ToString().Trim();
                    columnThree = selectCommandResult.GetValue(2).ToString().Trim();
//Etc...
                }



}
catch (Exception ex){
throw ex;
}

Might I also suggest you make the habit of keeping one naming convention per project. IE the below variable names you've given :
thisTable
p_mobile
alt_ID
argID

Should all be one convention like:
tbTableName
pMobileParam
pAltIdParam
pArgIdParam

It will make it easier to read in the future.

Further reading: http://msdn.microsoft.com/en-us/library/system.data.sqlclient.sqlcommand.aspx[^]