Confederate Reports of the Fight - They Claim to Have Beaten Sickles, and Taken a Number of Prisoners.

The Richmond Inquirer of the 26th inst. has the following brief account of the engagement:

Contrary to the prediction of the knowing ones, no general engagement took place yesterday. A considerable fight, however, did occur, between 7 and 8 o'clock in the morning, on the Williamsburg road.

We gather the following particulars from an officer who was wounded in the engagement, and brought to this city yesterday afternoon.

The 22nd Georgia regiment, which was on picket duty, was attacked at an early hour and driven in by a vastly superior force of the enemy, when the 4th Georgia was ordered to its support.

With this force engaged on our side, the fight lasted for some time, when the 1st Louisiana regiment was ordered up to their support. Arriving on the field, Col. Shivers, of the Louisiana regiment, gave command to his men to charge the enemy.

The order was promptly obeyed, the men charging with spirit and determination, in solid column, and receiving the fire of an entire brigade of the enemy, and sustaining a heavy loss in killed and wounded.

Reinforcements were then promptly ordered to the front, and the enemy was driven back with heavy slaughter. The last reinforcements sent up, we believe, consisted of the 25th North Carolina and several other regiments, who fought nobly, sustaining a slight loss.

A portion of the force engaged was the notorious drunken brigade of Sickles.

The engagement lasted for about two hours, and is said by those engaged in it to have been very severe. We have been furnished with the following partial list of casualties in the First Louisiana Regiment:

Col. Shivers, severely wounded in the right arm; Captain O. Cornier, company I, slight wound in the left arm; 1st Lieut. J. Taylor, company I, wounded in the right leg; Adjutant Cummings, wounded in the right leg; 1st Lieut. M.B. Gilmore, company E, killed - he was shot through the left ear, and died almost instantly; 2d Lieut. Joseph Murphy, company F, killed; Lieut. Wm. Kendrick, company G, killed; Capt. Randall, company K, wounded in right arm.

The loss in killed in this regiment is supposed to be about thirty. We could not obtain an estimate of the wounded, but it is supposed to be very heavy.

Four different color-bearers, in this regiment, were shot, but each time the colors were caught by one of the color guard, and flaunted defiantly in the very faces of the enemy.

The regiment was highly complimented on the field for its bravery by Gen. Wright. ...

The Dispatch of the same date says: The enemy, advancing their lines, suddenly fell upon our pickets, and owing to superior numbers, drove them in upon our supports.

The advance of the enemy was composed of Sickles' and another brigade. Informed of the state of things, the First Louisiana was sent forward to reconnoiter and find the enemy's force, position and intentions - but to do this their journey lay across a large open field, and while advancing, the cowardly enemy screened his forces in the thicket, and having caught the gallant First Louisiana in the ambuscade, delivered a murderous fire, which struck down dozens of the valiant fellows.

But not dismayed at this reception and their heavy loss, the brave men instantly dressed their line, dashed at Sickles' hirelings with their bayonets, and routed them.

Still opposed to greater numbers than their own, the 1st Louisiana was quickly supported, we are informed, by the 3d, 4th and 22d Georgia regiments, of Wright's brigade, who held a large force of the foe at bay for two hours before our forces were got into position, and appalled the enemy by their formidable front. Except in the 1st Louisiana we hear of few casualties, and this arose from the fact that they were the victims of a trap laid by the Yankees, and were too heroic to fall back when discovering it. Col. Shivers, Major Nellegan, and many men were wounded. Lieut. Gilmore and some others being killed.