Understand what makes the chord
F major contains F, A, and C. You do not need six ringing strings to establish those notes. On the top three strings, the third string at fret two, second string at fret one, and first string at fret one provide A, C, and F. This compact voicing can support a song while you develop a larger barre shape separately. Strike only the intended strings, since an accidental open low string can change the bass and make the result sound less settled.
Use xx321x without changing the chord quality
Try xx321x in standard tuning. From low E to high E, omit the first two strings, fret the D string at three, G at two, B at one, and omit the high E. Those three sounding notes are F, A, and C: a complete F-major triad. Use ring, middle, and index fingers respectively. Pick only strings four, three, and two, or brush those three with a narrow strum. No six-string barre is required for this voicing.
Build an original four-bar practice phrase C–F–Am–G, one bar per chord. On the F bar use xx321x; for the others, choose familiar shapes and keep one attack on beat one. Listen for the change in register, not just whether the fingering is easier. A compact F will sound lighter than a six-string C, so narrow the surrounding chords or lighten their attacks if the F seems to vanish. The aim is an intentional accompaniment rather than one conspicuously thin emergency chord.
Practice the partial barre gently
Use the index finger to cover the first and second strings at fret one and place another finger on the third string at fret two. Experiment with a small rotation of the index finger rather than increasing pressure immediately. Pick each note and release between attempts so that the hand does not remain clenched. Practice moving from a nearby C or A minor shape into this small F. Keep the wrist comfortable and stop if the exercise causes pain rather than ordinary learning effort.
Choose the size that serves the song
Play the small voicing with the melody and listen to whether it provides enough weight. In an ensemble with a bass instrument, a compact upper voicing may fit especially well. For solo guitar, you might later add a lower F note or learn the full barre when you need a fuller sound. Treat the larger shape as another option, not as proof that the smaller one was invalid. A clear three-note F played on time is musically useful. Expand it when your arrangement, technique, and comfort make the extra strings worthwhile.
F and Fmaj7 are not interchangeable
Do not substitute xx3210 without noticing the change: the open high E adds a major seventh, making Fmaj7. That color can be lovely, but it is not identical to F. Likewise, xxx211 gives A–C–F with A lowest, an inverted F voicing; it may work well with a bassist supplying F, but its bass character differs in a solo part. Name and choose the version you actually play.
Fit the small F into your demo
For your Suno demo, first verify that the disputed chord really is F and not F minor or Fmaj7. If you have an authorized MP3 available under your account's download rules, AudioChords can supply a starting chord chart and guitar diagrams for checking. The recording may contain a bass instrument that lets your three-note voicing fit naturally. For an unaccompanied version, decide whether that lighter bass is acceptable before learning a larger grip. Add strings only when the arrangement needs them and the shape is comfortable.