Since Category-6 is specifically UTP (Unshielded Twisted Pair), then the question of shielded Category-6 cabling doesn't make any sense. ANSI/TIA/EIA define the cable categories, and there are no cable categories defined except for UTP.
The ISO/IEC defines cable classes, and it has defined several classes that employ a shield.
Having said that, many cable manufacturers will offer a shield on their cable to try to make up for poor cable performance (would not pass the test suite without the shielding). If shielding is used in cabling, it must be continuous from end-to-end, with no breaks, and grounded, at least, on both ends. The equipment on each end must also be compatible to ground the shield.
There are documents that explain things for you. For example, Shielded and unshielded twisted-pair cable revisited:
If STP cable is combined with improperly shielded connectors,
connecting hardware or outlets, or if the foil shield itself is
damaged, overall signal quality will be degraded. This, in turn, can
result in degraded emission and immunity performance. Therefore, for a
shielded cabling system to totally reduce interference, every
component within that system must be fully and seamlessly shielded, as
well as properly installed and maintained.
An STP cabling system also requires good grounding and earthing
practices because of the presence of the shield. An improperly
grounded system can be a primary source of emissions and interference.
Whether this ground is at one end or both ends of the cable run
depends on the frequency at which a given application is running. For
high-frequency signals, an STP cabling system must be grounded, at
minimum, at both ends of the cable run, and it must be continuous. A
shield grounded at only one end is not effective against