Without code it is hard to know what you want or what you may be doing wrong. But filling the area between curves just needs the call to fill once you have defined the path.
Example
const ctx = canvas.getContext("2d");
const unit = (a, b, u) => (b - a) * u + a;
const p1 = {x:20, y:420}, p2 = {x:480, y:20}, p3 = {x:20, y:480};
ctx.beginPath()
ctx.moveTo(p1.x, p1.y);
ctx.bezierCurveTo(
unit(p1.x, p2.x, 0.5), unit(p1.y, p2.y, 0.0),
unit(p1.x, p2.x, 0.5), unit(p1.y, p2.y, 1.0),
p2.x, p2.y
)
ctx.bezierCurveTo(
unit(p2.x, p3.x, 0.5), unit(p2.y, p3.y, 0.0),
unit(p2.x, p3.x, 0.5), unit(p2.y, p3.y, 1.0),
p3.x, p3.y
)
ctx.lineWidth = 3;
ctx.lineJoin = "round";
ctx.strokeStyle = "#F80";
ctx.fillStyle = "#08F";
ctx.fill();
ctx.stroke();<canvas id="canvas" width="500" height="500"></canvas>