I work frequently with really small sashings and borders, some will finish at 1/4 inch or just under. A few tips. Starch these prior to cutting , and I mean STARCH the daylights out of them . I use the concetrate full strenght for this type of work allowing it to air dry for the best stiffness. Then use a foot that allows you to needle over , so that the bulk of your fabric is under the foot, using the foot edge as a guide.
Sometimes depending on the width is it better to "ride the ridge", having the ridge under the presser foot and making the adjustments with your needle.