You will want to set whatever column has your "LAST MODIFIED" values as the Maximum Value Column in GenerateTableFetch. The first time it will still generate SQL to pull the complete data, but it will also keep track of the maximum observed value from your Maximum Value Column. The next time GenerateTableFetch runs, it will only generate SQL to fetch the rows whose value for LAST MODIFIED is greater than the last observed maximum.
If you want the first generation to start at a particular value (for the Maximum Value Column), you can add a user-defined property called "initial.maxvalue.<maxvaluecol>", where "<maxvaluecol>" is the name of the column you specified as the Maximum Value Column. This allows you to "skip ahead", and from then on GenerateTableFetch will continue in normal operation, keeping track of the current maximum and only generating SQL to fetch rows whose values are larger than the current max.
If you need a custom query (or, more correctly, you want to add a custom WHERE clause), you can do that by setting the Custom WHERE Clause property of GenerateTableFetch. If you need completely arbitrary queries, then in NiFi 1.7.0 (via NIFI-1706) you can use QueryDatabaseTable to provide arbitrary queries. This capability does not exist for GenerateTableFetch, but we can investigate adding it as an improvement, please feel free to file a Jira for this.
